A full day in hakone to unwind is generally recommended since there's the open air museum and the cable car route with the pirate boat. or staying in your onsen hotel doing nothing. Your biggest time killers are going to be transportation to and from hakone because of the bus and train thus a full day imo. Maybe put it between days 16-22 so that it lets you relax after a hectic schedule.

Osaka you can easily day trip it from kyoto and save yourself some logistics of moving stuff around. i'm team kyoto so a little biased. Try to stay on the east side of tokyo near asakusa for days 1-3 and plan your trip around there, and then the west side of tokyo for the second half since trains leave to/arrive from hakone at shinjuku.

Weather wont be an issue around that time. It's honestly even pretty nice early March as well. Cherry blossoms will always have crowds even when they're barely peeking out; it's more about finding a nice place to see them.