Legal Question in Real Estate Law in California

No, only the owner of the unit can make a reasonable request to enter and do work needed with the least amount of disturbance to you. If the work to be done is not something needed to remedy a habitability problem, then even the owner probably can not enter while you are still in possession. You have a right to peaceful enjoyment of the unit.

No. The soon to be new owner is not the owner until escrow closes. Then that owner has to give you reasonable notice of their desire to enter, and must follow the same laws and rules that governed the former owner as a landlord.