6) Any must see, do or eat things as a honeymooner visiting in July?
Yes.
Ask your concierge to make an evening reservation at Ukai Toriyama in late June (best) or early July. It's already one of the most beautiful restaurants in the country and fireflies are released into the grounds in June/July.
http://www.ukai.co.jp/english/toriyama/
Before or after your visit you can get the rope car/train to the top of Mount Takao and visit the beer garden/bar, at 500 metres it's the region's highest.
http://www.mount-takao.com/beermount/
Mount Takao is particularly easy to get to from Shinjuku.