Consequently, how do you promote AMVs?
Post on other AMV related forums (not just your video, become a part of that group, make them love you first and then your work), kiss a lot of ass, or become good friends with any other talented/well-known editors and hope they pimp your videos for you.
Also Know, can you monetize AMVs? You can't monetize AMV's and in theory it's illegal to make them however you can find AMV's on anime cons, which are supposed to be official events so I guess studios don't really care of AMV or at best will ask for a delete of the video.
Similarly, is making AMV illegal?
It's only illegal to distribute an AMV (when you don't have the rights to the footage and music). Making it, showing it to your family/friends (no, an online community does not fall under the description of "friends"), and talking about them are not illegal. So, feel free to list it, just don't offer a download option.
Are AMVs protected under fair use?
Pretty much all amvs have a gray area when it comes to copyrights. They're somewhat protected under the Fair Use clause, but they also aren't completely protected.