Off the top of my head I would say only if you are a co-broker. As a referring agent you are not an agent of the buyer. But I would check my state's laws.

Check your stste laws. Normally it is illegal to pay an unlicensed person.

Questions like this should not be discussed by agents with each other and if the question is being asked by someone outside the industry then again it should not be answered.

Yes if they are a party to the transaction and with full disclosure.

Do it regularly! It must be disclosed to both the buyer and the seller.

I am sure they can do whatever they want to with their fees.

I know some companies base their business model on giving back part of the commission.  I'd advise to check with your state's lawyers first.  In California the state association has a legal helpline that you can call.  I'll assume other states (or your larger agencies) have something similar.

Yes for CA,  have to be documented in writing, disclosed and usually refunded to them via escrow( or used in any other way the buyer chooses)

In my stateYou can credit it to the buyer through escrow but not outside of escrow.

Not on the HUD, shouldn't happen.

No, here in Kentucky you can't.

All depends on if it is legal by the state, I know to pull it off you'd need to get into the grey area in the states I have a license in.

As you have seen in the other comments there are several issues involved:

# 1 Is it legal in your state.

# 2 Does the lender know, is it on the settlement statement.

# 3 Does your office policy / broker allow it.

It is a better policy to complete the transaction at settlement. You need to check on the rules in your state and the policies of your broker.

I would add any money back to buyer that is over $500 would receive a 1099

yes and they incur taxes on it. in escrow they can  with brokers approval (doubtful)

Yes, at least in Florida.  Other states may have different rules.