Generally speaking, "to be *on to* something/someone" means that you have the right idea about something or someone. So yes, in the context of a person, because you have the right idea about that person, you can anticipate what that person will do or how that person will behave. You can use it for situations where you are theorizing, and the person thinks that what you've said makes sense. "To be *on* something" is different (no "to"). That suggests that the person is under the influence of drugs or some other mind-altering substance. There is also "to be on/off one's game", which suggests that everything is going very well/badly for that person at that given moment. It usually applies to sports or games, but it can also apply to situations where someone says or does several things correctly or incorrectly in succession.

You got it. The expression is “to be on to someone” . They are trying to deceive you but you are aware of that. A wife who learns her husband is having an affair could tell him “I’m on to you” My Mom’s on to us. She knows we’re not getting together to study.

You got it right.