On weekends yes. I believe it is the case on weekdays too but am not sure.
True also on weekdays. Even the express service Trenton to New York first stops at Hamilton and Princeton Junction before heading non-stop to Newark.
Yes--Princeton Junction is my commuter stop, and every NJT train stops there (as well as Hamilton)--I've done the commute on weekdays and weekends. (There usually is a huge crowd trying to get on as I get off!
) Also, Princeton Junction is a very pleasant station--small, safe as far as I know, and nobody will ask what you're doing if you just sit on a bench and watch trains go through. I've even seen people with tripods filming at the end of the platform, and nobody has said anything. It's much, much nicer than Trenton, and certainly much better than North Philadelphia. (The only robbery seems to be in the "convenience" store, where they charge Princeton prices!) The platform going south is less busy/crowded than the one going north, so that is where I would sit. The only problem might be parking--check first about where you can park just for a day and how to pay for it.