Yes - but it's not direct. You have to go by way of New York City.
Yes, Amtrak's Keystone Service operates frequent, high-speed trains between Philadelphia and Harrisburg.
http://www.catchthekeystone.com/
Newark, NJ either downtown or at the airport. Both are on the Northeast Corridor.
Lancaster. From there you can take the Keystone Service west to Harrisburg and east to Philadelphia or New York, or the Pennsylvanian west to Harrisburg or Pittsburgh and east to Philadelphia or New York.
Amtrak trains do not go to Bangor. Amtrak Thruway Bus service is available three times a day from Portland, ME.
Yes. Amtrak runs both Regional trains and Acela express trains, with the Regional being cheaper but taking a little longer. Use the link below to access Amtrak's page that will let you see all trains available -
Go to amtrak.com to buy amtrak tickets.
sorry but no
Yes Amtrak goes into Michigan; main part follows the I-94 corridor.
Yes, except for some corridor trains like Amtrak Cascades.
On Amtrak, a one-way train ticket would cost about $50 each way ($100 round-trip). If you buy the tickets a few weeks in advance, you can probably get them for $40 to $45 each way. See the Related Link below for the Amtrak homepage. In the "From" field, type "NYP" for New York Penn Station, and in the "To" field, type "HAR" for Harrisburg, PA.
Yes
Yes, it does.
Lancaster, PA. It is on the Keytone Service, Pennsylvanian and Capitol Limited such that you can get there directly from New York, Washington, DC, Philadelphia, Pittsburgh, Cleveland and Chicago.