I’ve never seen things move before, but I have have had the TV turn on and off by itself (multiple instances on different televisions) before with nobody home but me (not near any remote control). This has also happened with my stereo it would start playing music.
I have also had items switch off (house buzzer) which requires someone to manually move a switch forward until it clicks (happened 4x), when I was the only one in the house and the door locked. Each time someone walked by my house the alarm would go off, and it was really driving me crazy, so I turned it off. It switched itself back on. So, I turned it off, and switched itself on again 3 more times. There isn’t a breaker related to the system, it requires a hard press over to the right, and requires strength to do. I don’t drink, nor do I do drugs of any kind. I’ve also had a glass cup which was sitting on my dining room table, shatter into pebble sized pieces when there was nothing in the cup and it was placed in almost the center of the table (there were multiple witnesses to this).