Kyoto schedule seems a bit aggressive/optimistic to me. Fushimi Inari is worth it, but can be very tiring, particularly if you go see the whole thing up to the top.

An alternate to Hakone for viewing Fuji: Kawaguchiko. I'd say Hakone is more interesting overall, but Kawaguchiko can provide better views of Fuji, if that's a primary driver. All that said, given your tight timeline, I agree with the sentiment above that it's probably not worth dedicating a set day to see it.

IMO Tuna Auction is a bit underwhelming, but I don't discourage people from going to see it. If you want to see it, go see it. It's a big pain to go and the experience is short. Be prepared for that. But if those facts don't scare you off and you want to go still, then definitely go. I'd plan to arrive well before 4. Maybe 3:30. I guess it varies considerably.

Probably not what you had in mind but there are a pair of 1-star restaurants in Tokyo that each provide a full meal for under $15 - both Ramen restaurants in the Sugamo/Otsuka area. Honestly, unless your tastes are very strongly aligned with Michelin's, I've found them to not be all that helpful in Japan.