Questions for those who've been to Japan.

Been there several times, for weeks or months so from my point of view :

1 : Cool isn't the right word. Let's say it's interesting.
2 : Like SenorKaffee, I should say minimum 2 weeks, one week is enough for Tokyo while you need more time to discover the "real Japan".
3: Kyôtô and Nara, no doubt.
4 : It's recomanded to get japanese notions, since their english 90% of the time is worst than mine (which means close to awful). Also you need a trustworthy map to travel there. An example : At Tokyo once I asked my way to a cop, the cop was quite embarassed and asked to another cop, who asked to a third cop. Also, you should get issues with the subway plan at first, but after a while you'll get used to it. A good avice would be to take the Japan Rail Pass if you plan to get outside Tokyo.
5 : It's up to you ^^ But it would be a shame to stop only at the Akiba crap while the countryside is awesome. Also Tokyoites got a very weird (stressed+cold) mentality compared to the people who live in the west side of the country (warmer and friendly).

Jam it back in, in the dark.