As above, for your question about f4.0 - 5.6. Constant aperture means that the lens retains a 'constant' (the same) aperture throughout the zoom range and doesn't vary with the focal length. It's good to have, but constant aperture lenses are generally more expensive and sometimes a lot more expensive!
It can actually be looked at both ways;
Constant F-Stop.... remember the aperture is the hole size, and that is very rarely 'constant', even on a prime, fixed focal length lens its norrmaly a variable diameter iris; on a zoom lens where the f-number may be 'constant' throughout the zoom range, it's still got a variable diameter apperture to let you set different f-numbers..... confuddling terminology, innit?!?!?!
Anyway, can be looked at both ways, as I said, and a constant through zoom f-number, lens will tend to be a more expensive lens....
for the same fastest f-stop
Longer lenses tend to be more expensive; they give more magnification, so the glass has to be more curved, which means thicker, and more difficult to shape. They also need a much bigger aperture behind them to give the same f-number, so to make them even reasonably fast, they have to be bigger in diameter as well as thicker and more bowed; meaning harder still to make, and make accurately enough to give decent results.
Remember the maths; F-Number is aperture diameter divided by focal length; so on a 50mm lens you only need an aperture of 25mm or about an inch to get the reletively fast f-number of f-2, one stop faster, f1.4 still only needs a 35mm hole, so you can get that in a lens that has a barrel diameter under two inches.
OK, lets scale that up to 500mm.... to get a fast f2 f-number we need a hole diameter half the focal lenth... 250mm, almost TEN inches, and our lens would have to be almost a foot accross the barrel. That a LOT of glass and its gonna be heavy, as well as unweildy, as well as expensive to make.
But, using compound lenses, rather than making one big chunk of glass with a big bow in it, and sticking it a long way from the film-plane... sorry 'sensor'... if we use two or three or four smaller, more mildly bowed bits of glass that are cheaper and easier to make, they each multiply the magnification, to give the same effective magnification as a big long single element lens...
BUT we get a double whammy; some of those bits of glass are going to have to move forwards and back to let us change focus.. BUT we can use those same 'movements' or perhaps introduce an extra one or two, and changing the focal length between a couple of elements, multiplied by the others, gives us a Variable-Focal-Length lens or in common parlance... a ZOOM!
Now, multiplying magnifications to give an 'effective' focal length through a group of lens elements rather than just one... well, the aperture size is going to similarly be effected by these magnification effects, so where its placed in the lens in relation to the moving elements is going to change it's 'effective' size, and possibly its effective size in relation to the zoom setting. Hence the sums not adding up on many modern lenses according to the theoretical ratio.
However; placing the aperture to get a constant f-number can impediment the lens makers options to improve lens performance, or it may mean that within the constraints of making a lens reletively compact and lightweight, they may have to compromise the fastest aperture setting to do it.
Or they could just get down and dirty; I mean, my 18-55 kit I think is a 3.5/5.6 F-stop lens... they could, if they thought that people would percieve it a 'better' lens if it has a zoom setting independentfastest f-stop... simply put a limiter in it, so it was f5.6 fastest aperture setting accross the zoom range... same lens.. but the idea that 'constant f-number' must be better, would imply that that actual removal of functionality made it some-how 'better'... which obviously it wouldn't... hence looking at it the other way; and
zoom-dependent fastest aperture settings, can be looked at as a 'bonus' giving you a 'bit of extra' where it is possible, almost for nothing.
It's not necessarily 'Bad' or necessarily 'cheap'; it's just where the compromises in the lens design have been made; and a constant through zoom F-number doesn't necessarily mean a 'better' lens.
