Legal Question in Wills and Trusts in California

Partially, it depends on what the trust says. They often require both signatures. If it is a communtity property issue, half of the property might be transferable by one party, but not the entire property. Would need much more info to give a thorough answer.

Probably requires all trustees' signatures.

in order to answer this question, the trust agreement and all amendments need to be reviewed.

The trustee is the party who signs a deed that transfers property out of a trust. You use the term "trust deed" which is California's financing instrument, commonly called by lay people a "mortgage." I assume that you are transferring property out of a trust, using a deed. The trustee, or all trustees if there is more than one, are the proper people to transfer property out of a trust. If you meant "trust deed" or "deed of trust" the financing instrument, then you need to repost and clarify.