Legal Question in Real Estate Law in California

No. Only a broker can use MLS, and only after paying the substantial membership fees.

Mr. Nelson is correct. I would add that most lenders will not negotiate a short sale if you haven't used an agent and listed on the MLS, because your chances of getting the best price without doing that are about zero. Since all the money will go to the lender anyway, why do you care about a commission?

There's no law against doing your own short sale. However, lenders generally want some conformation that the selling price is close to full market value, and will distrust a deal in which the owner, rather than a broker, has negotiated the price and terms. Also, brokers that do a significant volume of short sales have key lender contacts and can get quick approval (or a quick rejection, for that matter) which may be necessary to close the deal before the buyer moves on to another property. As to using MLS, however, keep in mind that it is a broker's organization and not open to do-it-yourself sellers.