You serve at the behest of the President.
Ahh, nope. He has a six year term. He can be impeached, I guess. The whole reason for the six year term is so the President can’t fire him.
There will never be 2/3 of the senate ready to convict him.
So, pretty much he is here for a while.
FBI Directors
“They must be confirmed by the United States Senate and serve a term of office of five years, with a maximum of ten years, if reappointed, unless they resign or are fired by the President before their term ends. The current FBI Director is James B. Comey, who was appointed in 2013 by Barack Obama.”
My bet would be that Trump doesn’t want another “Senate Confirmation Witch Hunt” at the moment, but will get around to Comey in due time. I will also bet that he already has developed a list of replacements.