1) To get to the vatican you can walk to the piazza barberini or spanish steps (about 10 minutes to either)and take the metro to the ottaviano stop. This will put you a block or so away from the entrance to the vatican museums.
2) It is about a 15 minute walk from the trevi fountain to the pantheon. It is about the same to get to the colosseum from the pantheon. I would suggest walking to both.
3) It will be about a 20 minute walk to the train station if you choose to walk. It is all down hill so if you are pulling luggage it will be pretty easy. You can also have a cab take you. The fare should be less than 12 euros.
4) If you are visiting 2 sites and using the transport part of the pass then you will save money. The best part of the pass is that you will bypass the lines to get into the colosseum and forum. This alone for some people is worth the price of the pass.
5) The kids don't get any discount on the pass or the sites. The only place they will get a discount is at the vatican museums which are not covered by the romapass. The pantheon is free as it's a church.
Make sure to book entrance tickets or a tour of the vatican museums before you go to bypass the line outside. Make sure to make a reservation to the Borghese gallery and use the call me back button to book with the romapass.
Donna