Depends on where you're starting from. From my town, it's about $8.50 each way to/from Penn Station, and it's usually a 35-40m ride (edit: assuming NJTransit is on time, lol), with roughly hourly trains on weekdays and every 2h (plus a transfer) on weekends.
If you're starting from down in (e.g.) Princeton, though, it's going to be more like $19.
Yes, but it's not a huge savings. 10% on a weekly pass (so only worth if if you're coming in all 5 days) and maybe 25% for a monthly (assuming you're in 20 days in the month).
And this is one of the best transit systems in the US. Now you know why people are freaking out about not being able to drive -- the other options are there but limited