I apologize for the late response. These past few days have been rather busy for me.
The first questuon i had was how have we established these two categories of things that exist and have a cause vs. Things that exist and don't have a cause?
Something is
“necessary” if it could not possibly have failed to exist. The laws of mathematics are often thought to be necessary. It is plausible to say that mathematical truths such as two and two making four hold irrespective of the way that the world is. Even if the world were radically different, it seems, two and two would still make four. God, too, is often thought to be a necessary being, i.e. a being that logically could not have failed to exist.
Something is
“contingent” if it is not necessary, i.e. if it could have failed to exist. Most things seem to exist contingently. All of the human artefacts around us might not have existed; for each one of them, whoever made it might have decided not to do so. Their existence, therefore, is contingent. You and I, too, might not have existed; our respective parents might never have met, or might have decided not to have children, or might have decided to have children at a different time. Our existence, therefore, is contingent. Even the world around us seems to be contingent; the universe might have developed in such a way that none of the observable stars and planets existed at all.
The argument from contingency rests on the claim that the universe, as a whole, is contingent. It is not only the case, the argument suggests, that each of the things around is us contingent; it is also the case that the whole, all of those things taken together, is contingent. It might have been the case that nothing existed at all. The state of affairs in which nothing existed at all is a logically possible state of affairs, even though it is not the actual state of affairs.
It is this that the argument from contingency takes to be significant. It is because it is thought that the universe exists contingently that its existence is thought to require explanation. If the universe might not have existed, then why does it exist? Proponents of the cosmological argument suggest that questions like this always have answers. The existence of things that are necessary does not require explanation; their non-existence is impossible. The existence of anything contingent, however, does require explanation. They might not have existed, and so there must be some reason that they do so.
if it is possible for anything other than your God to be a member of the set of existing non contingent things
Yes, it is possible. However, nothing in modern science has been able to have any explanation that does not violate the Laws of Thermodynamics or the Laws of Conservation of Mass and Energy.
Finally, is it reasonable to propose a god as a possible cause of the universe... I would say no because we don't have evidence that a god exists. Why or why not?
I would disagree. I can't tell you how many times people have made the claim that "we dont have evidence that a god exists" when in fact the evidence is everywhere. I would argue that "evidence" is subjective based one one's level of skepticism. Another issue is the question of what would "evidence for God" look like? What would you consider to be evidence for the existance of God.
Actually the argument doesn't assert anything about the cause, at best it implies them but we are getting ahead of ourselves

The first questuon i had was how have we established these two categories of things that exist and have a cause vs. Things that exist and don't have a cause? There could be a begging the question problem going on in premise 1 as well which is why I asked if it is possible for anything other than your God to be a member of the set of existing non contingent things and I don't see an answer to that question either. Finally, is it reasonable to propose a god as a possible cause of the universe... I would say no because we don't have evidence that a god exists. Or put another way, would it be reasonable to propose universe creating pixies as the possible cause for the universe? Why or why not?