What is the constitutional basis for the inherent powers of the federal government

They were assumed by the writers of the Constitution to be necessary to the government to function.

both are true, the congress does have the power to create banks, even if this power is not specifically described in the constitution, since there is nothing restricting it and there is power given to the congress to make "all laws which shall be necessary and proper". maryland was not allowed to tax a branch of the national bank operating there, and the supreme court decided that no state could. both of these topics were discussed in a decision of the mcculloch v. maryland case in 1819.