Pretty damned awesome of you.
I wouldn't know the answers that you seek, and I don't know if anyone else can definitively answer them either, since things vary from department to department. Some departments are quite lax about personal firearms, others are very strict.
Have you considered calling the PD and asking to speak to a Lieutenant or the armorer? You risk ruining the surprise that way, but you'd get reliable answers. Unless it's a big city cop shop, I'd bet they'd be happy to talk to you about it. Just make sure you explain your family relationship or they might be suspicious of your inquiries.