Looks alright to me for the most part.

Your 13 May schedule seems a bit busy but most probably doable (mind you I haven't been to all of the places you listed).
On the other hand, your 14 May plan is rather scant and I think you should add in Kiyomizudera, walking down from it along all the shops into Gion.
Fushimi Inari will be more like 1.5hr hike round-trip to cover most areas of interest, unless you want to go all the way to the top or you're extremely slow walking.

If it were me, I'd overnight in Hakone on 20 May to thoroughly enjoy the onsen experience and to give yourself more time to enjoy Hakone.