I am not licensed in CA, but I think you're asking a great question. Common law fraud requires intent; if you did not intend to commit fraud, then I do not believe the act was created. I would suggest that of you do not have an attorney, you should immediately get one.
I am licensed in New Mexco and Pennsylvania, and therefore any discussion of issues related to other states must considered within that context. In addition, my comments are not intended to create a legal representation but merely to respond to the limited facts presented by the question. Any opinion herein is not meant as a precise statement of legal rights or as a recommendation of any particular course of action. A more complete legal review can be obtained through local counsel.
Fraud requires an intent to commit fraud, and that can be hard to prove. This could be breach of contract, but this is harder to prove based on an oral agreement without anything in writing since the terms of the contract, from what you describe, seem to be in dispute. If the oral contract is void, or if no contract was formed, there could be a cause of action for "quantum meruit", which basically that the contractor is entitled to the reasonable value of the job; otherwise you would be unjustly enriched. Once the complaint has been answered by the defendant, the plaintiff has to request leave from the court to amend the complaint. These cases are very fact heavy and not so simple, so you should really consult an attorney.
All information provided is for general purposes only and does not establish an attorney-client relationship.
This is probably not fraud, unless they can show that you did not intend to pay them and they relied on it. It may be breach of contract.
A plaintiff can change their theory of the case and their claims as they go along, it does not require filing another suit.
If you are being sued, you need to contact an attorney in the area. Try to find one that handles construction cases since you probably have a some defenses that other attorney might not be aware of.