Legal Question in Real Estate Law in California

This is insufficient information to give you a decent answer. Basically, an offeror should be signing his own offers. However, as an exception, a duly-authorized agent can sign papers to commit his principal. The additional information needed was whether this real estate agent represented you, and the scope of the representation, and in particular, whether you gave the agent permission to make and sign this offer on your behalf.

Actually, you didn't even ask a question. I'm just assuming that you mean to ask whether an agent can sign and offer on your behalf. The answer is that a principal (like yourself) can authorize an agent to enter into almost any kind of transaction for him. A licensed real estate agent, working for you, could sign offers on your behalf if (a) specifically instructed by you to do so, and (b) the agent did not violate any professional rule in so doing.

I should also add that most agents will sign their own names, adding that they are acting on behalf of so-and-so as principal. When the agent signs the principal's name directly, the agent must have specific authority for that act, and in so signing, the agent acts as a so-called "amanuensis" which is legal Latin for someone who signs a principal's name at the instruction of the principal.

Not without a proper Power Of Attorney from you, and even then it is unwise.

And your question is?