(Sorry for the long delay!)
1. I think the main thing which dictates the limits of construction is not how the world is, but how WE are (which, since we are part of the world, is perhaps the same thing, but we'll let that slide for the moment...). So, what constructions are logically possible are dictated by the limits of logic, which is in turn dictated by the limits of who we are, as human beings. So, we will always be limited, to an extent, by the nature of our existence as biological entities, and the practices that are important to us as a result of this. For instance, for some reason we are curious beings, who seem to need to know all sorts of things (such as whether reality is constructed or not!). Such a need is driven by who-knows-what - a vestige of an evolutionary process that has been useful for survival, or even (to take a religious possibility) a God-given drive to search out 'truth' - who can say? But whatever the cause of the need, the fact that there IS one determines a limit to our enquiries. Put simply, to get an answer, we have to set boundaries - without some sort of rules to the game, it's difficult to play! So, one limit upon construction is the need to make things work for us (which is in turn related to a mysterious impulse to know).
Another limit on construction is the self. The world is a different place depending on what we experience/conceive the self to be. Buddhism and certain Hindu philosophies have quite a radical attitude to this: the self - or rather Self (a universal entity, with a capital S) - is all that exists; the rest is illusion (construction?). What determines our notion of reality therefore is that which we separate our self from. Descartes thought that the experience of an individual, thinking entity represented an irreducible fact (i.e. NOT a construction), but subsequent arguments have disproved this, I think. Therefore, what was fundamental for Descartes is not fundamental (non-constructed) for us. Why is this? It's because our notion of self is different. But the same might be said for the Buddhists and Hindus, so this isn't a case of scientific progression!
I'm aware I'm skating over topics here, but these are slippery things to talk about. Feel free to home in on one or two things and we can try to be more specific.
2. Well, there are two questions here, you naughty boy! They are linked, but can take us off in different directions. Firstly, my religious beliefs are personal not in the sense that they are secret or immune to rational investigation, but rather that I try (for the sake of discussion) to keep them separate from philosophy. In other words, I don't want people to think that I always have a religious axe to grind, or am not willing to entertain radical possibilities.
However, your 'second' question relates to this: my views are actually very broad and fluid. I am not confined to one orthodox viewpoint, such as Christianity or Judaism, but rather feel it important to consider these questions from a rational perspective. To say (as, e.g. Thomas Aquinas did) that natural reason will definitely lead us to the truth of faith is itself an act of faith, and I wouldn't want to go that far - we have to at least entertain the possibility that (for instance) reason and faith are at variance, or that reason is even incapable of (by itself) establishing religious truth. However, I do think that we should be very wary of abandoning reason - it may be a cop out to say that certain truths are beyond reason's reach, and may even involve a sort of paradox (how do we know? how can we prove that?). Therefore, even if there are limits to reason, this is something that reason can prove (such as with Godel's incompleteness theorem in mathematics, which seeks to rationally prove that maths (and by extension, logic) has no ultimate rational basis). Therefore, I would say that my position is closest to someone like John the Scot (Johannes Scotus), a 9th century Irish philosopher who said
authority proceeds from true reason, but reason certainly does not proceed from authority. For every authority which is not upheld by true reason is seen to be weak, whereas true reason is kept firm and immutable by her own powers and does not require to be confirmed by the assent of any authority.
More specifically, as for how the problem of constructivism affects religious belief, I don't think it does (at least, not mine). There is, as I've suggested, a long tradition, spanning many faiths, that sees reality as a form of illusory construct, resolving into a constructless divine reality which is, effectively, indistinguishable from nothing (just as an infinite substance cannot be bounded). Does that make sense? However, the discussion we've been having is perhaps not about absolutes, but about knowledge - and, as I've tried to suggest, knowledge requires limits, and is related to self.
As to the details of my religious convictions, I'm happy to discuss them, but - as I've suggested - they are not fixed articles of faith, but rather rationally decided possibilities. If you have specific questions, please ask, or perhaps we can have some debate on religious matters in the philosophy of religion part of the forum.
Sorry for the very, very long response...!