1. Sorry, I am not much help on this one, probably. I stayed at the Shangri-La by the main station (would be over the $300) and the Intercontinental Bay - decent hotel, location fine for me, but it is certainly not much stuff going on in the area.
2. I believe you can buy full rate Japan Rail tickets outside of Japan, through travel agents, but not ones using the JR pass. I have not done this, I used a JR pass.
3. I purchased a SUICA card from a machine in Tokyo station - a 'pay as you go' card similar to Oyster card in London - you can use it on local rail, subway, buses, in convenience stores etc. Found it very simple to use.
4. I really liked Nara, so if your trip means one more night in Kyoto to do so, I would make the change.
As to the website, I booked three hotels through Japanican with no issues whatsoever.