Your question is actually a dozen different questions all folded into one another. I am tempted to skip all of your post aside from the last sentence, since that's what you wasted so many words trying to get to, but I will instead answer every sentence with a comment.
>How do you reconcile your faith with the discoveries of modern science?
Faith, i.e., trust in God's Providence, is not in conflict with higher sensual faculties such as reason. To assert so is to make a category error. If, for example, it were true that faith and reason conflict, then pious people would not be able to use reason to construct language and write as I am doing now.
>I mean Biblical cosmology, at least in Genesis, views the earth as pretty much just land under a dome with the eternal waters of chaos surrounding it and the sun and moon and stars within the dome making that pretty much the whole universe.
The people who wrote the Torah, i.e., the first five books of the Old Testament, were ancient Hebrews who spoke using metaphors and allegories, as well as via things they could observe to draw parallels. E.g., the Earth does indeed appear, when you are standing in a broad plain, like a flat surface topped by a dome. The fact that ancient people wrote what they saw should not be shocking or surprising. Accordingly, if I say that a road is "flat" would that be an error? Technically, not even flat surfaces are flat at the microscopic level—ultimately, this is all a question of semantics. It's like asking if a tree exists. Technically, "tree" is a made-up human sound.
>Later in early Christian times, under influence from the Greeks, Earth was seen as the center of everything with the seven planets (the moon, the sun, Mercury, Venus, Mars, Jupiter, and Saturn) revolve around it in seven different layers.
Again, this is how it appears to be when your only tool of observation is literal, from-the-ground eyesight.
>Later it was discovered that Earth and the other planets (except the moon) actually go around the sun and that's it's not a planet but a giant fusion reactor fire ball 1,300,000 times larger than Earth. Then it was discovered that actually there are many other solar systems out there besides ours, millions even billions or trillions! Then only in 1929 was it discovered that other galaxies besides our own exist, again possible millions and billions.
And almost everyone who made these discoveries was a devout Christian. The size of the universe is as relevant to religion as is the rotundity of a tomato. It's a footnote.
>Einstein's theories make it probable that the universe is infinite (though this doesn't make an infinite amount of matter) and there are probably trillions upon trillions of galaxies out there.
The universe cannot be infinite in dimension, as evidenced by red shift. It has a measurable size in three dimensions, albeit a large and expanding one. As for the number galaxies, again; it is as relevant to the existence of God as the number of insects.
>On top of that numerous earth like planets have been discovered.
So what? There are oak trees, and then there are pecans and pines and mahoganies. Diversity within Creation is a feature, not a "glitch" as you seem to presuppose.
>On top of that quantum fluctuations predict a universe that can create itself out of nothing….
According to what study? With what certainty? Don't do make of these arrogant "pop science" mistakes of finding a snippet of disembodied information and using it to support a tangential hypothesis.
>So seeing that we humans are extremely insignificant within the grand scheme of things and that actually we are not the center of it all how do you reconcile this with your faith?
Insignificant according to whom or what? In what way? Can't you see you've already decided on arbitrary standards for the designations of "significant" and "insignificant" and then applied them to this subject in order to justify your unbelief?