ok, my thoughts are:
1. go to akihabara and harajuku, theres usually loads of ppl cosplaying around there. akihabara coz of all the maid cafes, and harajuku coz of all the teens. also, theres loads of anime conventions all year round that u can find out about easily and get to.
2. no idea- never saw anything like that when i was there
3. roppongi and shibuya i liked best, but it depends on the individual. i personally love roppongi (i'm an 18 year-old female btw) but alot of ppl think it's too westernized and full of drunk ppl, but i liked the music, the number of clubs, and meetin ppl from literally everywere on earth. its also open all night, and u always come back with stories!!!
plus its great if ur single...
4. way too many places to say... but i do recommend getting away from tokyo at least once, i absolutely loved going to hokkaido for afew days and visiting onsen. and my number one place in tokyo that i must have been to about 10 times while i was there was shibuya- the best shopping ever!