From TF Green Airport train to Back Bay. 1 h 20 min $11. From Oakland Beach Opp Victory line 3 bus to Kennedy Plaza, walk to Providence Amtrak, then train to Boston Back Bay Station Amtrak. 2 h 5 min $142. From Warwick drive to Cambridge. 1 h 12 min $6.
Yes, there is a direct train departing from TF Green Airport and arriving at Back Bay. Services depart every 4 hours, and operate every day. The journey takes approximately 1¼ hours.