I was in LGA last year, not a "new guy", but a junior 73 captain, so probably about the same reserve life.
The Domestic and International divisions in NY are still separate. You can bid between them, if there are vacancies. The international is a much smaller division, so they probably don't fly as much (but you can still be used for domestic trips on reserve).
Yes, you will cover all three airports. It seems like the flying I ended up with was mostly JFK and EWR, much less out of LGA.
EWR had at least two trips that reported at 04:00 on the first day. The JFK trips had a little of everything. There was a PHX 3 day slash trip, with an all-nighter home on the last day that always seemed to be in open time.
The flying in NY is good, the crews are great, but having to cover EWR is a PITA. Unfortunately, on the 73 there are only two bases where you won't have to cover three airports (DFW and ORD) and both of them are very senior.