1. Osaka to Tokyo is a 3 hour trip on the Shinosaka line
2. HALF a day in Kyoto? You might want to reconsider this. Especially since your going to stay 3 weeks in Japan. Even if you dont like culture and history you have to. Spending a week in kyoto should like you 2 weeks for Tokyo which is a good start. Kyoto is the cultural capital of Japan. There is so much to see that you could spend A LOT of time there.
Then theres the surrounding like Nara. I mean just google Kyoto or pick a book about Japan and look for Kyoto and youll understand.
For exemple look over here:
Kyoto Travel Guide
3. Like you said. This question as already been answered a lot of times over here. Just take a look in there and have some fun ! Japan guide books are also usuful.
Sorry if my answers arent so helpful but the most important thing i can tell you is the really reconsider the time you want to spend in Kyoto. It doesnt matter if your a techno-electro-skyscrapper-megacity junkie that dont like culture, history and that kind of stuff. You HAVE TO see the temples, shrines, gardents and etc. in Kyoto. Hehe
have fun