There are several questions here and there are several different domains of philosophy involved. One major question is about ontology: is what we call 'free will' a 'real' experience and what's the difference between that and it being 'only a perception'? There's a broad range of thoughts on this, some of which veer into theology, but also things like "functionally we're so complex that we have effective free will, regardless of strict determinism in the process of reality" to "the question is irrelevant, because the only thoughts that actually matter are statements that make scientifically testable predictions."
For the latter case, experiences don't imply anything because they are outside the framework of our discourse, so to speak. Discussions of qualia (what it feels like to be conscious and making apparently free choices) are irrelevant because they make no testable predictions and therefore have no empirically accessible truth. Personally I find this perspective a tad bleak, as it seems to relegate a lot of profound experience (as often expressed in art) to being essentially nonsense.
Another perspective is to say that conscious experiences, including the experience of free will are either identical with or emergant from the physical happenings that we can model and make predictions about. Since these happenings become quite complex once enough systems are interacting, the effective experience is one of free will, because the esssence of choice finds itself expressed through the sheer complexity of our decision making that generally precludes our ability to predict in advance how we will act.
This does raise an interesting question, though; if we had greater mental capacities and better models, to the extent that we could reliably predict our own behaviors, would that eliminate our sense of free will? It's not hard to imagine that this might, as one finds onself continuously acting out the sequence of events that intuitively have been foreseen, though one might also argue that at this point, the perception of present vs. future becomes blurred and is more a continuum perceived at once, a rather alien perspective compared to our sense of being caught in one moment, with an unknown horizon before us.
As for whether there is some reason why the perception of free will would exist, should it not simply be a consequence of complexity, one could argue that any sense of self which does not develop a concomitant sense of being a free agent would be in some sense self-defeating and so it's a natural consequence of any sense of self-awareness that develops. If I can truly model myself as wholly deterministic and predictable, then I no longer have any real need to think of myself as a 'self' at all, since I and my environment operate perfectly fine without 'me'. Personally, I find this thought less bleak than relegating qualitative experience to irrelevance and in fact this is a common theme, particularly in religious/spiritual philosophy.
I recognize I haven't very directly addressed your questions, but I think that's largely because these questions cover a lot of philosophical ground. There are whole books written on various topics in Metaphysics and the nature of consciousness and free will are some of the thornier subjects to discuss.