I'll second that BOS and LGA crews, in general, rock. Smallish bases, great Chief Pilots. That all goes for LAX too. Not so much for DFW and ORD.

If you are on reserve, no matter what base, yes you may be sent to another to cover flying. If you get LAX, you WILL be sent to DFW if on the SF3, or to DFW or ORD most likely if on the EMJ. When I was reserve in LA on the Saab, I think about 1/3 of my time was spent covering DFW trips.

As for instructing on the side, that's a no no. It counts toward your weekly, monthly, and yearly limits (30, 100, and 1,000 respectively). So of course the company doesn't want you filling up your available hours with outside obligations. It is in the FM1 that it is prohibited. IF you do it, then don't tell anyone, and do not log it.