It sounds like you left your apartment for the summer and came back to all new roommates and to what probably feels like random new rules for your own home. But it’s their home too.
Keeping shoes in the doorway isn’t safe. It’s more likely that the other girl’s grandma broke your shoe rack by tripping over it or falling on it than by moving it. If you want shoes for the common area why not just leave them just inside your door instead of just outside it? You have a whole room to keep your stuff in.
When your roommate moves coffee that you left on the counter for a few hours or moves your frying pan off the stove she isn’t just randomly moving stuff. She’s cleaning up after you. If all of you put your dirty dishes in the sink until you get to them other people can use the counters and stove. And if you wash the dishes and put them back in the cupboard people can use the sink.
It sounds like you feel like you can’t put things where you want in your own home, but the only things being moved are dirty dishes and shoes that you leave in the common area. Try to look at it from your roommates’ perspective. What you call randomly moving stuff they probably call cleaning up after you. Why is it such a big deal to put your dirty dishes in the sink and keep your personal belongings in your room?