You would charge the costs of repairing the damage or replacing the door. Generally, you would deduct from that charge the amount by which the door had depreciated. But the expense of the paint job is, I assume, minimal, and otherwise doors do not really depreciate.
Yes, you can.
Has the tenant already vacated or is the tenant still there? If you wish to deduct from the tenant's security deposit, you need to do so and provide the tenant with an itemized deduction within 21 days after the tenant moves out. (See CA Civil Code section 1950.5).
Frank W. Chen has been licensed to practice law in California since 1988. The information presented here is general in nature and is not intended, nor should be construed, as legal advice for a particular case. This Avvo.com posting does not create any attorney-client relationship with the author. For specific advice about your particular situation, please consult with your own attorney.