As an Umpire I talk to the players quite a bit:
-At the end of a play,"play's over, roll off easy."
-Before the play starts, I will work with the linemen as I stand over the ball to make sure I don't step on them or they don't step on me (still looking for comfortable steel-toed football shoes) linebackers to ensure that we won't be running into each other, and the safeties to ensure I am not blocking their view.
- I will inform players that there is an issue with their equipment, but will not assist them in fixing it, though I will ensure that they have a chance to correct the issue or they will be sent off the field to do it.
-I will offer verbal congratulations on good plays, and will check with the players who appear injured.
I try to avoid physical contact with the players as much as possible because of how that contact can be perceived. I would never pat a player on the behind. I don't think it is appropriate behavior for an official. That seems too "familiar" for lack of a better term, and I believe there should be some separation between player and official.
About the only time that I have touched a player is to lead him away from a potential confrontation and redirect him back to his huddle. But even in those instances I am uncomfortable, because I could be seen as restraining one player allowing the other player to take a shot.
At the end of the game, I will usually wave to the players and congratulate them on the game and wish them luck next week. I will not initiate a handshake, but if a player wants to shake my hand, I will do so.
I may be overthinking these things, but I have found it better for me to avoid contact, and try to stick to general instructions when communicating with the players.