David

In general, the phone policy is the norm now of days because too many people abuse that privilege. You are expected to work at work and there's no need for personal cell phones or calls during non-break time (AKA the entire time you're at work [outside of lunch time]). If there's an emergency then the caller should call you through your desk phone so the call is monitored and logged (otherwise ... it's not an emergency).

@marcelm the OP stated he's in the US so there's no need to mention European regulations when they will never apply.

Do you have other offers or prospects? Do you want to work at this company? Do you have prior experience in the industry? Do you have any problems on your background? Seems routine and straightforward for any sensitive position or one with access to valuables. Is there a reason you won't consent to these terms?

Perhaps it is rapport building or just poking fun? It's very common. There's only one side presented here and it seems like you have not taken steps to work with him/build rapport with him. I think this is a question that is too opinion based on someone we don't know and cannot know their side to be answered. Maybe your personality just is not a good fit

I would not bring "male vs female" gender into it either since there's no evidence to support that and the PI cannot present their side.