When should I arrive in Lake Kawaguchiko?

I'm planning to take a short one month course in Kyoto in the month of May, and is now starting to plan out the trip.

The main question I have is I'm flying out from Tokyo, and on the last weekend in Japan, I plan to go from Kyoto to Lake Kawaguchiko, spend the night and then onwards to Tokyo. I'll use luggage forwarding from Kyoto to Tokyo and only take a backpack with me. I want to visit Chureito Pagoda, Oishi Park, and go on the Mt. Fuji Panorama Ropeway. Do I have enough time to do all these activities if I arrive around 2pm, and leave around 1pm the next day? Or should I take the overnight bus and arrive around 9am? Overnight bus would be less comfortable so I'd prefer daytime travel if time permits.

Also, do you think 300,000 yen in cash is enough for a month for one person? I'll do large purchases via credit card, but want to avoid repeatedly taking money from ATM and getting hit with multiple f/x fees, atm fees, etc… I'll be spending mornings in class, and afternoons & evenings wandering around Kyoto, Osaka and Kobe. Also weekend trips to Nara, Kanazawa and Hiroshima. I love to eat, so that should be the bulk of my cash expenses aside from transit.

Thank you in advance!

by konami_27