DPI should really be PPI or Pixels per Inch, however as your software is using DPI I will continue to use that term.
300 DPI means that the image, when printed, will have 300 dots (pixels) for every inch. If the printed image is 10 inches wide then the supplied image has to be 3000 pixels wide (3000/10 = 300). If the printed image is 5 inches wide then the supplied image has to be 1500 pixels wide (1500/5 = 300).
You need to know what the size of the final image will be, you can then supply an image with the correct number of pixels.
Printed Image width (inches)/300 = number of pixels width.
It can be confusing until it suddenly clicks!
Imagine a tile mosaic on a wall, it is 30 inches wide and 20 inches high.
Each tile is 0.5 inches square. There are therefore 60 tiles by 40 tiles, or 2400 tiles in total. The resolution is 2 tiles per inch or 2 TPI.
If you want the same mosaic but larger and still use 2400 tiles you have to have larger tiles eg. for a 60 inch by 40 inch mosaic you will need tiles that are 1 inch square. The resolution is now 1 TPI.
If someone wants a resolution of 3 TPI and a mosaic that is 45 inches wide by 30 inches high you have to have 135 tiles by 90 tiles or 12150 tiles in total.
If they just say they want a resolution of 4 TPI it does not help at all, they need to also tell you the final size that they want or how many tiles in total you can use.
Not sure if the above will confuse you more but I hope it helps
As for raw, in simple terms raw gives you better editing options.
When you want to print, or display, raw you convert to jpeg anyway.