It's from psychology: it's where an intelligence develops a model of a thing and then mentally simulates what will happen to it given X. Caledionian crows are capable of developing mental models in solving problems, for example. A mental model of a person is basically where you've acquired enough information of them to approximate their intentions or actions. (Or you might use existing archetypes or your own personality for modeling--put yourself in their shoes.) For example, a lot of the off color jokes by Jimmy Carr would seem malicious from a stranger, misogynist, or racist, whereas you can see with someone like Carr that the intention is to derive amusement from the especially offensive rather than to denigrate a group.

Not a conscious technique. When you get to know a person you form some kind of brain structure which allows you to imagine that person when they aren't around, and which makes some behaviors seem more realistic/in character for them than some other behaviors. This structure is your mental model of that person.

I use this phrase a lot; in my case it's just a turn of phrase. Can't speak for anyone else, though.

Sorta both. Basically your mental model of someone is anything internal that use to predict their (re)actions.