First time in Japan - two week trip!

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Hello! I am beginning to plan a trip to Japan next year, and I’ve decided two weeks would allow me to get the most out of my trip. Most of my stay will probably be in Tokyo as I’m a bit of an otaku (“a bit” is probably a massive understatement but I like to stay modest) so I can explore Ikebukuro and Akihabara thoroughly. As such, I have a few questions I would really like to sort out before I start putting things down on paper.

1. I can only visit in the summer as I’m in college, so does anyone out there know what time of summer would be best to visit? I’d be most interested in times when anime (especially idol) related events are happening, but general advice is much appreciated as well!
2. When is the best time to start making reservations? I’ve heard it’s best to book international flights 6 months in advance but I am not sure if this is the general unspoken rule.
3. I might be buying a lot of stuff while I’m there What’s the best strategy for traveling cheap (i.e. mostly capsule hotels if I can) while carrying a suitcase? While my main destinations are Ikebukuro and Akihabara, I’d like to explore all of Tokyo as much as I can. I’d like to keep my belongings somewhere safe while I’m out, but I don’t necessarily want to be restricted to one hotel for my home base.
4. Well… Is my plan of two weeks in Tokyo too unrealistic? I’ve never traveled outside of my home country before and have only been to “big” cities a handful of times, so I don’t really have much reference for what to expect. I’m going to try and pack as lightly as possible so I don’t have to lug a heavy backpack off the airplane and into the city, but I figure inevitably I’m gonna have to buy a suitcase and have to lug that around, hence question 3.
5. Also, I’m not sure how much this matters since Japan recently changed the age of majority to 18, but will any hotels or businesses in general give me a hard time since I’m 20?

Sorry if my questions are outside the scope of this forum. Really, any advice would help me as a first time international traveler. Thank you in advance!