Salem

$5 in the parking structure. $4 in the municipal lot

There is a direct train from several Northern Indiana cities to Boston, and several other trains from parts of Indiana to New York City or Washington DC where you can transfer to trains to Boston. Once in Boston you can take subway or bus routes from South Station where the Amtrak trains from south and west arrive, to North Station where there are local trains to Salem Station.

The train doesn't go to south station, it goes to north station. It takes 30-35 minutes to get to north station.

Yes you can.

No there aren't.

There is a train at 6:35, take it to Boston and switch to the Haverhill line.

Look at 465 schedules on mbta.com. The buses don't run on Sunday however.

An hour before you need to be there

check the 455 bus schedule on the MBTA website