@Lisa5061 Just as you would expect hosts to respect your boundaries, a guest also needs to respect simple things that have been asked of them, like turning off lights, turning down heat or AC when not at home. If a guest is respectful like that, a host would have no need to feel they should enter the guest space. When you say it's your paid for, private space, if a guest is running up an electricity bill that is twice what is normal and what the host budgets for, then your "paid for" space becomes "not really paid for."
That said, I would ever enter the guest's space to do something like turning off lights, myself. I would only enter in an emergency situation, which excess usage of utilities isn't. But I can also understand a host who has repeatedly and politely requested a guest not to be wasteful, only to have their requests consistently ignored, getting so fed up with the disrespect that they go in and turn the lights off themselves. Respect is a 2 way street.
I'm very sorry if you had your personal items go missing, that's wholly unacceptable- it would even be unacceptable for a host to touch a guest's stuff, unless they were moving it out of the way of a burst water pipe or something. But please try to understand that in a home-share situation, the guest usually has access to some shared common spaces with the host, as well, so the host's stuff is just as vulnerable to being messed with or stolen as a guest's is. It's all about trust and mutual respect.