I'm afraid your questions are too full of imponderables for any definite answer. There also are some aspects that I am afraid you will have to clarify before they can be discussed sensibly; for example, how do you see matter existing before space, given that matter is mostly space?
The question of whether the universe is infinite is not fully clear. When I was at school I favoured the "steady state universe" theory of Fred Hoyle and his associates, and in fact I still rather like it, but modern cosmology favours the Big Bang, and the evidence eventually became so strong that even Hoyle more or less capitulated. One implication is that the universe and its content are by no means infinite.
So it seems that your question or questions start from a wrong assumption anyway.
However, suppose that the universe really were infinite, the effect on what we observe need not be very decisive. We could not see beyond the red-shift horizon anyway. Any part of the universe notionally beyond that distance might as well not exist for all the difference it would make to us. From some points of view it could be argued that they would not be part of our universe at all.
Again, we might be living in an observable part of an infinite universe, but at some fairly close distance beyond our horizons, the average density of the matter and energy in space might decrease for about the same distance as the radius of our observable part of the universe, to such a degree that that extra space contains only half as much as the space that we observe. Then at the same distance beyond that, the density could halve again and again. If this went on for ever, no part of the infinite universe would be empty, but the total would contain only about twice as much matter as we could in principle observe, which most certainly is very finite.
Such an infinite space would topologically be open, in that, no matter how far you went, you could always go further away without ever getting closer to where you started. Whether it would be open in the sense that the matter would not collapse on us would simply depend on whether it currently is expanding fast enough. If it is not, then tough luck; there is a Big Crunch coming! If it is in fact expanding too fast to Crunch, then tough luck for other reasons!
In a Hoyle-type steady-state, notionally infinite universe, the question of whether it would be open or closed would depend on its average density and rate of expansion and continuous creation.
To resolve any such points that you might find interesting, I am afraid you would have to be a bit more specific. So far it is not so much a question of what you mean, as whether what you have said is in any way meaningful.
Give it a good thinking over, and let us know when you think you have learned to recognise some of the holes.
