I hate it when... We add "it" because of a specific annoyance.

Yes, it sounds correct and natural! Alternatively, you could say: "I hate it when someone takes my personal things without asking." Both versions work well depending on your style preference.

This is fine, It can also be written as; I dislike when someone uses my personal things without taking permission.

Sounds good. You can shorten this to, “I hate when someone takes my things without asking.”

Yes ! :)