To answer your first question: In order to create a map, you need to use Warcraft III World Editor. To learn how to actually execute the process of creating one is complicated...and I have found is better to learn through personal trial-and-error. If you wish to make a map, come up with an idea and then go find tutorials on this site on how to do the things you wish to accomplish (such as how to make the map look like it's under water...or a tutorial on basic triggers)
To answer your 2nd question: You use Warcraft III RoC or TFT. The first is the original (classic), while the second is the expansion. I recommend the expansion since most everyone has that. In order to make a map, you need Warcraft III World Editor, but do not worry, that comes with both the classic and expansion version.
Yes, people often play DOTA, but that is just the way Battle Net works. Lots of people play DOTA