Here is a hint regarding terminology. Refer to the sellers agent as the listing agent. Theyt are listing the property and representing the sellers. In California, a seller may offer a cooperating broker a commission as well. The proper term for the cooperating agent is commonly referred to as the selling agent (yes that is the agent representing the buyer).
In California all commissions are negotiable. However understand that many conventional brokerages do not negotiate much on them. Your common large players will not do much. Remember that alot of players get a slice of the pie. The agent, the broker, the corporation.
So your tact if you want to approach the listing agent directly would be to ask for a portion of the coop commission, NOT the listing agents commission because that agent will be double ending the deal. Many brokerages will not let any parties be unrepresented, there is much to much of a liability.
So the answers to all of your questions are yes it is legal. Some agents may entertain the possibility and some may not. You can make it more enticing by doing it correctly and not asking for any of the commission on the listing side. Yes the proceeds can be used for closing costs as long as the lender okays it. Some may and some may not. You can also simply lower the purchase price by the amount.
Doing this in a letter will get you a 0% success rate. You will need to approach the agents in person at the open houses or call them. Your letters will go straight to the trash can. You can also just go with a Redfin to get a coop rebate or other places.
