Regarding #3, having a bank agent state on a recorded call “well, you don’t sound female” seems like a good way to get sued by a protected class.
If the bank in question has literally never dealt with federal funds (e.g. FHA mortgages) then they may be exempt but this does not apply to most consumer banks.
EDIT: The Equal Credit Protection Act and the Fair Housing Act explicitly covers gender and sex as protected classes. Very few consumer banks in the US are not covered by these acts.
Technically but not materially true, since gender identity discrimination, like other forms of conformance-to-sex-stereotype discrimination, has been found by the Supreme Court to be a form of sex discrimination.