Legal Question in Real Estate Law in California

That would depend entirely on the terms of the purchase and sale contract between you. Also, even if they don't have a legal right to do so unilaterally, they and you are always free to agree to mutually acceptable terms to extend COE.

It's not at all unusual for escrows not to close on the originally agree-upon date, and while the delay is most often due to the buyers not having their money together, seller-caused delays are also fairly common. Most often, reasonable delays are accommodated by the other party, often grudgingly, but they's rather get the deal done than see it fall apart because of a week or two delay. Sometimes a party will compensate the other by paying rent or interest, or covering the costs of the party not at fault. Occasionally the deal falls apart and occasionally there is a lawsuit. Also, review the sale agreement and see if it contains a "time is of the essence" clause, any specific provisions for rent, interest, penalties for delays, or the like. Finally, if you have been represented by a broker, get the broker's opinion.

It depends on the purchase and sale agreement, which often are also the escrow instructions.