The principle of causality is not incompatible with the existence of free will.

From a physical point of view, the principle of causality is a statement regarding the time ordering of events which have some causal relation between them. Simply put, it states that effects cannot chronologically precede causes. If you take time as an absolute concept, this is a rather trivial idea, but in a relativistic model of the universe, which requires dropping the notion of time being absolute, different observers can make very different reconstructions of the history of a given set of events. What they absolutely need to agree on, in order for causality to be in place, is in finding causes happening before their respective effects.

Now this principle of causality is not synonymous with determinism, particularly causal determinism. Briefly, it states that every single event in the universe is a necessary consequence of a set of preexisting conditions which may be regarded as the causes of the event, and the event their effect. And while the principle of causality is profoundly embedded in any formulation of the accessible reality, probably because it reflects a basic feature of the universe, causal determinism is completely put at bay by quantum mechanics' description of the most basic constituents of reality that we know of.

At the quantum level, an event is not a necessary consequence, but a compatible consequence of a set of preexisting conditions. For a given configuration of a system at some given instant, there is not a single necessary point in configuration space for the system to move to. In a not very rigorous way, one can think of the system as accumulating potentials for evolving into a (possibly large) set of points, from which one is eventually chosen according to a probability distribution. Even though there are causal relations between events (in the sense of the principle of causality), there is no causal determinism in quantum mechanics, at least not in the classical sense.

Now, how does this relate with free will? A completely farfetched argument would be that the inherent uncertainty underlying the quantum mechanics' form of causality proves that there is free will. I think it should be easy to see how this is an unreasonable stretch. However, quantum mechanics does tell us that, at the most basic level that we are aware of, reality is not really deterministic, but more of a stochastic nature. If we assume that consciousness and, therefore, volition, operate on the basis of biochemical and electrical processes in neural networks, and that at least some of these processes occur according to quantum rules, then there is a lot of space for some level of non-determinism to be part of consciousness processes.

In summary, even if the classical realm of physics seems completely deterministic, free will might still be perfectly compatible with it, because at the smallest scales the apparently deterministic reality in which we live is actually a very fuzzy succession of probable configurations and outcomes.

If we are or not living inside the Matrix, that seems to be an entirely different question. If one can test this hypothesis, then it should be worth trying. Until then, I believe the question to be of no relevant consequence. If we were indeed living inside a Matrix and it was inaccessible in any way to us, whatever we might learn about how this simulated universe worked would be effectively indistinguishable from learning the same thing about a non-simulated one. So, give me some way to test it or just disregard it altogether.