Answer 1: I'm really cheap so I've stayed in Tokyo everywhere but a decent hotel :P

Answer 2: Why don't you try Odaiba, there are a lot of small shops over there. In your example you compared clothing shops, maybe it's my taste but when I lived in Japan I never found a decent Japanese clothing store, except for uniqlo. If you look for souvenirs, in Asakusa there is the souvenirs shopping street where you'll find everything you want. If you see something you like buy it! don't say "I'll find it cheaper somewhere else", it will be really difficult to find it, with some luck you'll find it 10% cheaper at the most and worst case you'll find it more expensive (happened to me )

Answer 3: Maybe you already tried it as you said you had been to Osaka, but, besides also trying good Izakayas that somebody may recomend, good place to go just to know something more are the Japense fast-food restaurants (Sukiya, Yoshinoya) that are everywhere, economical and it's interesting to eat Japanese fast-food. There are also the 180 Yen ramen shops, really nice and cheap ramen, just check the restaurant before hand as there are some really nice and decent (like to stay for a beer and talk with a friend) and some that are just to take the ramen and run :P

Answer 4: As things to do... pff, I've visited tokyo for like 30 days as a tourist and there are a lot of things that I'm missing: my
favorite spots:
-Tokyo Metropolitan Government observatories: completely free and amazing view, I didn't go to to the top of Tokyo Tower but I'm sure I didn't miss anything.
-If you need a rest of 15 minutes, take a coffee at the Starbucks in the Shibuya crossing, get the tables that are in front of the windows and amaze yourself (you can have a Grean Tea creem frappucinno without the watermelon flavor that they put in the US so you don't feel too guilty).
-gift shop of the NHK Studio Park near shibuya, the museum is 150 and entertains you for an hour but the cool thing is the gift shop, great things to be found there although not cheap.
-Ginza by night: this is the neighborhood for all the really cool and fancy stores, really expensive places to see there, but the feeling by night, with all the lights, for me it's just amazing.
-Roppongi Hills: Appartment tower but has a waaaay cool shopping mall inside, loved it!
-Tsukiji Fish Market: Really interesting place, some people say you can have sushi early in the morning from here after walking around the market, it will be expensive though. If not feeling like sushi early in the morning, just go to the market.

Have a great time there!