Probably not. Though, for a decade after that the Federal government was controlled by a key opposition party. Essentially they(people who accused him) had all the time to investigate him.
Difficult to say. For one, they aren't appointed by the government in power, but have created their own "collegium" system where one batch of judges selects their own replacements.
They've also restricted the government's ability to change this system.
At least in the US, the Supreme Court is anything but impartial. Judges typically vote along party lines.