> Compatibilists would reject 3) but would describe 2) as the exercising of 'free will'.
Compatibilism is "compatible with" determinism, it doesn't depend on determinism. So even if we turn out to be non-deterministic beings, that fact is irrelevant to Compatibilist free will.
The most common Compatibilist view is probably one that focuses on an agent's reasons for acting. If an agent acts for internal reasons, they are acting of their own free will (reasons are beliefs, judgments, inclinations, etc.). If an agent's reasons are subjugated to another agent's reasons (coercion), then they are not acting of their own free will.
Basically, Compatibilism is very similar to the way the law works. We judge whether a person's cognition is compromised in some way, and so whether they are "fit" and so can make choices of their own free will, and then we examine whether they actually did make a choice of their own free will in order to determine whether they are responsible.
(Not sure what you mean with "reject 3)" - they basically say it doesn't happen, and it need not happen for free will.)
The thought experiment is always "suppose we could turn back time, and arrive in exactly the same situation as we were before - could I have decided differently?". The traditional notion of free will sort of requires that you could have decided differently. The compatibilist notion of free will implies that, no, you could not have decided differently - but that doesn't mean that you have no free will.
EDIT to add: Sam Harris has a book about his version of compatibilism:
So for (2). If my psychological state is manipulated by a targeted advertising campaign, based on Google-scale data, do I actually have Free Will in any meaningful sense?
1) Where the decision is coerced.
2) Where the decision is not coerced and so ostensibly 'free' but determined by external factors (ie. the laws of Physics).
3) Where the decision is genuinely 'free', thus violating the laws of Physics as we know them.
Compatibilists would reject 3) but would describe 2) as the exercising of 'free will'.
Is that correct?