Legal Question in Real Estate Law in California

No. Once the trustee's sale goes through, a judicial foreclosure and deficiency action would violate the one form of action rule.

Not in the normal sense; an election to foreclose by trustee sale cuts off the foreclosing lender's right (if any existed) to seek a deficiency judgment. However, it is possible, but not very likely, that a lender might attack on a collateral issue such as loan-application fraud or malicious waste of the collateral.