I don't have time to answer all your questions but it seems Nagoya is the place to stay if you're seeing the Suzuka F1 race, it's about an hour or so by express train AFAIK, Osaka is another 30mins longer (or thereabouts). Much of a muchness in real terms.
So that being said, can you not land in Nagoya? You mentioned Toyko or Osaka... if it's only those two then yes, land in Osaka (Kansai Airport) and take a train to JR Shin-Osaka station (not JR Osaka) and there you can board the Bullet train to Nagoya. I've only satyed once in Nagoya at a Japanese style Ryokan in the city center, was a great place, very cheap and the staff were excellent. You may want to stay closer to the circuit though for the GP... which I can't make any recommendations sorry.
You could hire a car to go to the circuit but it may be a bit daunting if it's your first time driving in the Japanese country side... I'd want to be pretty handy with the car's navi system in that case. Anyway Suzuka city isn't a big place and getting to the circuit is easy by train from Nagoya station to Shirako Station, then to the circuit by taxi (takes about 15mins), all up assuming you have no problems it'll take about an hour, according to the circuit access guide on the Suzuka Circuit website.