Owner coming into my house when no one is home??

My boyfriend is currently seeking advice so I thought I’d share his story here.

“We moved into a new house beginning of this year, we’re renting and things have felt off for a bit. The house gives me this really odd feeling sometimes as if someone is watching. I thought it was because I was used to living in apartments but that wasn’t the case. I started noticing things being moved around the house after I would leave to run errands. Our laundry room has a door that leads to the side of our house but we’ve blocked it off because we needed the space. A couple days ago I come home to see the heavy bin that was blocking my door moved. I thought it was my mother but she later on questioned me why I felt the need to move it. Fast forward to a few days and the people that used to live in my house came by to pick up their mail. They got to talking with my mother and they told her the owner would come inside the house when no one was there to “check up on it”? I was more than freaked out since this entire time, I’ve been thinking there’s a fucking ghost in my house and turns out it could very possibly be the owner. The owners are my neighbors, they live in the house right behind me so I believe what they said. I don’t feel safe anymore & I feel angry that someone would think it’s okay to do that. I’ve thought about changing the locks or setting up cameras before we question her about the issue. I obviously want to have evidence to back me up. But am I allowed to change the locks since I’m renting? Would I have to give her a spare key? Should I check if maybe there’s cameras installed already in my home? Where should I check? I feel like if she’s bold enough to come into my house, she would be okay with setting up cameras. We’ve been paranoid ever since and I’m not sure where to go from here..”

We live in California btw