1. I just don't give my family name to a date.
2. I don't talk about work, it's rarely a deal breaker.
3. It's a normal thing to have a pied-a-terre.
4-5 Don't mix your friends-family and your date until you are sure in them. Actually, get an apartment on a different coast.
No, I don't think it's lying. And it's easy to do for someone with 8-9 figures in a bank.