[Reaganwuzthebest]

So space itself is most likely infinite, only the particles that lie within it, like stars and planets are finite, approximately 13 to 15 billion light years away?? So if a galaxy lies 100 or more billion light years away, despite the distance with our technology of today we would still be able to detect it?

[Physicist]

We may never be able to detect it. If the universe (defined not as all the matter we can travel to, but all the matter that exists) is infinite in extent, then--except for our local bubble--all of it is receding from us faster than the speed of light. We can never reach it, and its light can never reach us.

That's not to say that we can now see everything we could eventually see, if we last long enough. Some galaxies that are just beyond our current horizon will eventually be visible; we can't see them now because (as far as we can see in our reference frame) they haven't formed, yet. We can in principle watch the process of star and galaxy formation in the early universe, as the universe evolves. As the universe expands, however, the recession velocity of the earliest observable universe increases, and time dilation dictates that it evolve ever more slowly, as the velocity asymptotically approaches the speed of light. That puts a strict outer limit on the matter we'll ever be able to see.