I can give #3 a shot - you could take a train, then a short Uber. A train from Philly to the West Trenton station would take you about an hour. From that station to TCNJ’s campus is about 3 miles, maybe less. You can also take a train from the NYC area to Trenton (different train station location), and then uber/Taxi to campus.
TCNJ does offer some merit scholarship money, but it is very competitive, and I’m not sure if it is open to international students.
You should be able to find the answers to 1 and 2 on their website, or thru communication with the school directly.