Is giving resources away for free allowed?
Contrary to what mafu has stated in their answer, there is an official rule against this practice:


  You may trade with another player between your turns, but only if it
  is his turn and he elects to trade with you. You cannot trade with the
  bank during another player’s turn. You may not give away cards.


(from the Almanac section of the rulebook, near the top of p14)

I understand that you can "effectively" give away cards by cunning sequences of "legitimate" trades, but it seems clear that this isn't really in the spirit of the game, and players should feel free to frown upon such sharp practice!