Whats the Proper way to distribute textures? Should I directly compile them into the map? Or should I create my own WAD's? Do I need to get permission to use textures from other map or should I just make a note in the readme?

the best thing to do is compile them into your map. this prevents lots of problems and keeps your folders neat. If you sue new texture release them to the mapping comunity sepratly. Most texture artist are happy enough to be credited for their work in the readme.

give credit to the author and it's cool. However, you should never ever use textures from a different game (mohaa, rtcw, etc..)