Hamilton was referring to the SCOTUS. He supported it obviously, because a permanent Supreme Court justice is not beholden to the President or the Legislative branch of government. The idea is keep the judiciary "pure" from influence and/or control from the other 2 branches of government. Too bad it didn't work better.

Yes Hamilton supported lifetime appointment of judges to remove them from political issues as much as possible.

He means the right of judges to continue to hold their office, without dismissal or reduction in pay, for the rest of their lives.

He probably supports it.

Hamilton was a big government advocate.