Is it possible for me to call from a contract B, that has an instance of A, a private or internal function of contract A?
No, you cannot call a private or internal function in another contract.
private: only visible in the current contract
internal: only visible internally
Private functions can only be called from the same contract, whereas internal functions can be called from the same contract, as well as contracts inheriting from that contract. They are usually private or internal for a reason. If it's your own contract, you can create a public function in contract A, that you can call from B.