Legal Question in Real Estate Law in California

Of course; just like anyone else, subject ot proper disclosure of status. .

Yes. They must disclose that they are license holders and would probably be held to a higher standard of conduct, should a dispute arise, but licensees are not prohibited from dealing in real property for their own account, and many do, or did, when times were brighter.

The previous answers are correct. The key word in both is disclosure, not only of the fact that they are licensed, but that the transaction is a flip, unless there is a period of ownership by the professional after close of escrow on the professional's acquisition of the property and entering into contract to resell it. The one exception is that a real estate professional cannot flip a house to a person they are already acting as the agent for, since they have a fiduciary duty to let the buyer have the opportunity to buy from the original seller, and they should not sell property they own to someone who they have a buyer's agent agreement, though with adequate disclosures that is not always illegal (never really ethical though).