My question involves landlord-tenant law in the State of: California

I am a home owner and have a renter who rents a room in my 3 bdrm, 2 bath house. He has a room and use of a bathroom with common areas in the kitchen and laundry in the basement. He is moving out soon and we have not been getting along.

This week, I entered the bathroom in his area to fix the wall. I gave him a day notice that I was going to need to fix the area but he was not communicating. I also entered his room this morning because his tv was blasting and I could not sleep. I came home and he had printed out renters rights info about a landlord entering a unit and the conditions under which a landlord can enter. We do not have a written agreement but I have been letting him store some things in the basement (not apart of the original agreement).

1. Does his area qualify as a "unit"? Can I really not have access to the area and he have access to the rest of the house? What are my rights as a home owner?

2. Can I restrict his access to the kitchen and laundry in the basement even though at the beginning of the agreement, I said those would be shared spaces? I no longer trust him and feel he could retaliate by theft, etc. so I do not want him in my area with access to my things.

He also turns on the air conditioning when I'm not home and the bill is extremely expensive. I pay all utility bills. There are doors with locks that I have keys to in both areas that would restrict his access and also restrict his access to the air conditioning and heating controls. Is this legal for me to do until he moves out in 20 days?

Thank you.