1. GIMP is a good free alternative to Photoshop to work on layers.
2. I don't think there's really an "easy" or fast way about making maps. It does take time and you need practice and patience. You can hand-draw stuff, scan it, import in GIMP (if you choose it) and play with it in the software. Or you can try to draw it directly with mouse (not the easier way to do though)
3. Check Tutorial section, there's some interestinh threads about rivers, how to do themn how to place them and the basic rules you have to follow.
4. For what I understand about your project, you need your worldmap (probably a big scale so don't filled with details), then detailed maps ( nations maps/regional maps/cities). But if you're new to cartography I'd suggest to practice a bit before going on a huge project that can be hard to achieve at the first. Try to be familiar with a software (GIMP for example), use some tuts to learn some tips, make some practising maps and post WIP to receive advices and comments. This would be more motivating
Hope it helps