Yes - in private. Just after the closing.

My excellent service is their closing gift.

I dont.

Yes, I do.

It is a personal choice, but I can't see the circumstance under which another agent would even know you are giving your client a gift; unlesss you are doing so at the closing.  I would not pass on a gift at closing, unless it was upon your departure and transporting from your car to theirs.  Giving a gift to someone, in front of others, does not seem appropriate. 

Not understanding the other agents getting offended, have not seen anyone in my multistate experience get offended by a gift giving situation.

I give a closing gift to most of my buyers. I don't usually give a gift to a seller. 

I usually give gifts to ALL my clients, unless there are unusual circumstances. 

I don't give closing gifts to all clients, but when I do it is to buyers that I really enjoyed working with or had delays/issues to no fault of their own.  I leave the closing gifts at the home though, I don't bring to closing. 

It depends on the client.  I have had some clients that did not deserve a gift because of their actions and others, I have done way above what was in my description to do.

I give a closing gift to my buyer clients at their new home, it is either waiting for them in the new home or I stop by and hand deliver it.  I don't bring closing gifts to the closing.

You should keep your hand off of the other agents client. You could find yourself in the outer darkness, having difficulty scheduling showing, getting folks to answer your call or call you back and not realize how you got there.

Do I give closing gifts to everyone? No. 

Do I give closing gifts of great significance? You bet.

It is imperative that you let your focus be on your business goals and don't be distracted by what others do. Way to often the one coming in second place spent too much time watching the one who finished first. Don't be that person.

Now, what you are about to read is $600 dollar an hour guidance. I trust you see the value, if not now, at some point in the very near future.

"The greatest threat to releasing your creativity is the fear of comparison."

The self-talk in which you are currently engaged is the start of the constuct of the cage of your captivity.  Walk true to the light within you, and don't be distracted by the illusion of what lurks in the dark whose intent to devalue your vision, joy, worth, and purpose.