If you receive a favor token, you place it face down in front of you. However, you may view your favor tokens at any time to check which ones you have.
If I give a resource to an opponent for free, do I offer it to him openly or in a concealed fashion?
You offer the resource openly, e.g. by saying, “I'd like to give you 1 grain. Do you want to accept it?”
Yes, although that wouldn't be a very friendly action.
On my turn, am I allowed to immediately use a favor token that I received due to an opponent's road building action during the preceding turn?
Yes. The only favor tokens you may not use immediately are those you have received by means of your own actions during your turn.
The German game rules state that a player may use or exchange favor tokens only once per turn, while the English rules do not include this restriction. What is correct?
Favor tokens may only be used or exchanged once per turn.