Oh-Kay...
1a) the f1.4 isn't a full 'stop' faster than f1.8, so on that scale its not a huge difference, even if ultra fast apertures 'might' in the slim situations they can be.
1b) The big difference between the Nikor AF-S 1.4 and AFS 1.8's is price!!!! Some of that is that it is more difficult to make a faster aperture lens, but the bigger bit is actually the other way about; the 'faster' 1.4's are made to a higher general grade, so ts easier to incorporate the faster iris in them at the price they will command.
Ie they are two quite markedly variant grades of lens, and the f1.4 will almost certainly be technically the 'better' not because of it having the faster aperture, but it having the faster aperture because its the more expensive made lens.
2... 50mm and the crop factor....
The renaisance of the 'nifty fifty', contains a lot of legacy. Bear with the history lesson! 50mm is the 'standard angle' for a 35mm film camera, with a 45Deg Field of view.
You have to note that the 'standard', as in came with the camera, lens, wasn't always the 'standard' angle of view lens for that format; Particularly on fixed lens, 35mm cameras, the 'standard' lens that was fitted was often the more all-round versatile mild-wide of 35mm, while on a medium format 120 roll film camera, anything from maybe 80m to 110mm might be fitted 'as standard'.
However, the small, 35mm format, became popularized after WWII, as it used the same film stock as the movie industry, that provided a economy of scale to make the film 'cheaper' and provided affordable colour film. It also directed a trend towards more 'compact' cameras, but more significantly 'Single-Lens-Reflex' that used a 'periscope' mechanism of pentaprism and moving mirror to offer a 'Through-Taking-Lens' view-finder, which would have been large, bulky, difficult to manufacture and having to shift a mirror such a large distance out of the way to let light get to the film, likely slow, heavy and unreliable, on larger formats
35mm SLR's, came into vogue in the 1960's and '70's and were popularised through the 1980's to become the defcto 'enthusiast' camera; a lot of that born along by the fact that a Throgh-Taking-Lens view-finder made it a lot easier to make, and use, interchangeable lens cameras, where 'what you see s what you get', regardless of the length of lens fitted.
Most 35mm SLR's then came with a 50mm 'standard angle' lens in the box.. at that time, fixed focal length 'prime' lenses were the expectation, variable focal length 'zoom' lenses were not so common, and in that enthusiast market often critasised for their quality to 'save' carrying probably only one extra lens around.
As a 'sales feature' the low f-number of the 'kit' 50mm lens, was for a long time, treated with a similar mathematical reverence as Mega-Pixies are on digi-sensors today.. how useful that feature may be was often ignored on the assumption that a faster aperture 'must' make it a better lens... which often was true, but as above vs Nikon f1.8 vs f1.4 primes, not because the fast f-number automatically made it a better lens.
Through the 90's!!! Zoom lenses became more accepted, as they became 'better' and cheaper, and the marketing mens race for lower f-numbers was largely supplanted by a race for wider zoom-range. 'Normal' angle zooms that had generally had a 2x zoom range covering perhaps 35mm to 70mm about the 'standard angle' of 50mm, crept outwards to become 28-80mm 'ish' and the 2x zoom of old stretched to the 3x of the now common 'kit' lens on digtal. Meanwhile, Auto-Focus came into vogue on SLR cameras.
In the early 2000's... when 'digital' was evolving, 'crop-sensor' cameras based on the 'half frame' or APS film format were introduced to the consumer market, significantly because of cost. SLR cameras using these sensors frequently could mount 'legacy' lenses from earlier film cameras, which was a useful sales feature, to encourage existing photographers with a good collection of lenses for 35mm film cameras to switch to digital, and not have to invest 'quite' so much in a complete new system.
This legacy compatablity, sparked the renaisance in prime lenses, and partcularly 'fast aperture' prime lenses.
In the flm-only era, many cameras shipped with a fairly fast 50 as 'standard' that were very often very quickly replaced with a more versatile short zoom. Consequently, the value of 'kit' 50's was almost nil! (In the 90's you almost couldn't give away 50mm primes, especially older manual focus ones, more still ones in the less popular mounts!)
BUT; resurgent interest in photography kindled by digtal, coupled to legacy compatability with manual focus film era lenses, coupled to a wealth of 'accademic' excersises in 'how to do photography' books, usually written around the assumption that enthusasts would be starting with a 35mm film camera with 'kit' fast 50.. saw folk start to dig out and start using these 'cheap' legacy lenses, often ignorig the crop-factor, and exploiting that fast aperture for shallow focus effets hard to achieve with a smaller sensor camera without it, especially wth shorter, more 'normal angle' lenses for smaller sensor cameras.
SO!!!!!!!!!
We get to the question..s?....
- WHY do you want a prime?
- WHY do you want a 50mm prime?
- Why do you want a 'fast' aperture prime?
It's a bit backwards to the legacy questions, which essentially were that these lenses were available.. so what can you do with one! But starting with a crop-sensor digtal camera, and looking at brand new AF lenses for it, rather than available legacy offerings, it does really beg a clean sheet approach as if buying any other lens, for any other reason.
The 50mm focal length on a 35m camera, was always rather restrictive. The normal angle, giving normal perspectve, they were oft crtasised for creating 'borng' unflattering photo's, and always being a meddle in the middle; not being wide nor telephoto, and a one trick dog as far as wide aprture shallow focus effects went...
But, they were what so many accademic excersises were written for and the 'lessons' of those excersses to work wthin the limits of the gear you got, had merit.... But DONT when fitted to a Crop-Sensor DSLR... and the crop-factor sees a fast 50 offer the 'sort' of framing, but not the perspective of a short telephoto 'portrait' lens, usually around 80-110mm for 35mm film.
IF you want to mimic that fast-fifty experience and the academic lessons that were promoted by these, on a crop-sensor camera, a 35mm prime is likely the more appropriate tool.
A 50mm on APS-C, having the framing of a 75mm prime, is a bit short of a traditional portrait lens, and actually not providing the more flattering perspective in that situation of a 75 on film, its still a 50mm lens!
For shallow focus effects... fast aperture lenses are a go-to problem to a solution!.. and a fast aperture lens, probably ISN'T the best way to discover and explore that 'dissociated focus' effect... big difference between 'selective focus' and 'shallow focus'. Wider apertures do offer shallower DoF, but its only one variable in the mix, and a shallow DoF doesn't automatically put the subject in the sharp focus zone.. to do that you still need to exploit 'Selective-Focus' know how to get a DoF large enough to keep your whole subject in that DoF zone, ad get back-ground out of it! Expecting a lens to do the job for you, just because of a 'wow' fast aperture in the specs, is likely a road to madness, not actually achieving what you probably hope to very often.
RIGHT!!! tackling specifics....
I know this camera roughly has a crop factor of 1.5 which will effectively make my 50mm 1.4 essentially a 75mm 2.1 or a 75mm 2.7 if I go for the 1.8.
Tackling this one first.... The CROP FACTOR, gives a quick 'rough reckoner' means of comparison for the relative framing provided by different length lenses used on different format cameras; The focal length of a lens is the focal length of a lens, the aperture set on a lens is the aperture set on a lens... the 'crop factor' does NOT change these.
If you frame a scene with a 50mm lens on a 35mm film camera, putting that lens onto a crop-sensor camera does
not make it a 75mm lens! What you get, is the exact same 'exposure' the exact same focus, the exact same DoF... you just 'crop' top bottom and sides of the frame, so the image looks larger in reproduction!
If you want the same 'framing' on the crop sensor camera as you had with the 50 on full-frame... you would have to move backwards, increase your camera to subject distance; and if you moved back far enough, now your focus range will be longer, and at any aperture your DoF will be deeper, and trying to use the crop factor to work out how the perspective or DoF has changed just doesn't work... it depends on the camera to subject distance.
So even for framing, the 'crop-factor' does't go so far as your comment suggests, and it certaily doesn't have any bearing on the effectve f-number.
Now the question is, I want something that is going to be Superior over my f3.5(<s>actually 5.2f with crop taken into account</s>{No, see above!}) 18-55 kit lens. How much of an improvement will I notice
Oh-Kay.. I have the kit 18-55 on my D3200; for five years having hefted up to finally buy into DSLR and try and get the 'range' of lenses I have for my old film cameras, and just about got there; for the last six years, I have pondered the very same queston.. and that 18-55 is STILL on the front of my DSLR and my most used lens... I have REALLY struggled to find anything 'significantly' better in ANY practcally useful way to replace it with! Honestly!!
The Kit 18-55, has a very useful zoom range; it's lack of faster aertures is NOT a particular impediment for 99% of the photo's I take.. and having bought both AF-S35 and AF-S50 for my daughter doing O & A-level accademics, the biggest benefit of either, in my opinion is the brighter view-finder image!
As far as 'resolution' goes; I will concur that the high 24+Mpix offered by the later generation of widgetal cameras is starting to show up the 'limits' of the cheaper lenses, including the 18-55.... BUT... more expensive lenses aren't always 'better'..
Messing, I took some back to back shots with an old and 'budget' (Prinz Galaxy) M42 fit 'prime' on an infinity corrected adapter to compare to what I got with Nikkor 55-300... that old £20ish legacy less, even with a 'cheap' element corrected adapter literally blew away the Nikkor for ultimate IQ...
Large part of that is that the legacy lens was built for a full-frame 35mm camera, so the 'crop' sensor camera was only taking its image from the 'sweet spot' from the middle of the mage circle, and 'cropping' a lot off the edges where most abhoratios might have been more prominant; but, as an older lens, even a 'budget' one, when new that was likely made to a much higher grade and consumer cost, which was the only thing of importance, to buyers when the 'features' of variable focal length or auto-focus just weren't on the menu...
This does illustrate the anomoly; modern lenses with so much more demand for 'features' like zoom range, have to be built down to a much lesser 'grade', and optimised for a smaller sensor, helps them do that.
This offers conundrum IF you want higher IQ than a kit lens... shopping up the range, how much 'extra' IQ you may get is likely diminished by how much extra functionality they try pack into the product.. and you likely DON'T get such enormous gain in IQ for your money, you will get a lot more features and functions for it, with a smaller amount of added IQ over the 'acceptable' quality level of a lesser lens.
How much you may notice? ALL dependent on what you spend on what you buy.
I will say that back-to back, the IQ delivered by the 35 & 50 primes, over the 18-55 is, in 'most' circumstances, is 'noticeably better'.. but 'significantly' better? That's a very different question. And alone, either way, it isn't enough to make me buy either and faff more to use them! And applying that much extra diligence to use a prime, to using the 18-55, I would probably see a lot more overall 'improvement' in my shots, if little improvement to the 'resolution'....
So 'just' how much 'imrovement' do you want, or expect t see? If you cant do better wth what you got, buyng a 'better' lens probably wont do much of it for you...
And is it worth looking for the lesser condition 1.4 over the new 1.8...
2nd hand tends to be better value.. so IF either makes it onto the short-list, then, yes.. But remember, the f1.4 is the higher 'grade' lens, and that f1.4 aperture is a symptom of that, not the cause.
But the question, remains, IS a prime, is a fast prime, actually going to do what you hope it may?
As it stands, with the errors shown in your question, as far as the crop-factor and apertures, I would suggest, that you would find far more 'improvement' in your photography from learning, not spending.... Some photo books; a photo course and just getting out and about and learning from doing..
In that, following academic exercises for the learning, the AF-S 35, MAY be worth the punt, first to satisfy GAS, ad to give yourself something 'new' and inspiration to go play with it, and actually attempt the academic-exercises from tutorials, and gain some impetus to go so and try.. B-U-T... the 'gains' will likely NOT be 'in' the lens, but in your own approach and know-how to exploit it.
Remember its good photographers that make great photo's, not expensive equipment.
I'd also think about the "look" the lenses give, one may give a nicer look 
