I hope what you lack in manners you make up by being intellectually stimulating.
***Is this site dedicated to discussion about God and the nature of science, or what?***
This particular discussion God & Science forum traditionally discusses issues that relate to the 'big questions' which often include a discussion of the limits of science and assumptions of religion.
***If the universe is expanding and all galaxies are racing away from each other, then what is it that space is moving in to - God's home, his little bungalo of love?***
This issue is not resolved. Maybe space is infinite, or maybe it is finite. If finite, there would appear to be two possibilities. You travel in one direction long enough you end up where you started due to the curvature of space (this is perhaps the most popular current view held in cosmology), or you travel long enough and there is a sign that says "don't go any further!" [if you go further maybe there's a sign that says "I told you so"].
The expansion of space, depending on the model, is often viewed as an expansion into 'nothing'. That is, there is no physical laws or physical concepts (e.g., space) that apply to 'that' if you can even call it that. Other models have the universe expanding into 'parent' universes that existed prior to our universe (and presumably is still 'there'). Some string based models have the universe existing in multiple dimensions which even collide with other universes.
***What lies outside of the known universe?***
According to the inflationary model(s), there is a great deal of empty space beyond our known material universe.
***As the universe expands is it gobbling up this unknown area? Or is it that space is infinite and the matter within the space is contantly expanding outwords?***
Again, different models postulate different views. The Linde model of inflation suggests that universes are constantly inflating from false vacuums that occur somewhere in the parent universe. There are many other models.
***But that would mean time is eternal as well, wouldn't it? I thought that had been disproven.***
No general agreement about 'time' exists. As Augustine of Hippo said: "As long as no asks me [what time is], then I know what it is, but it someone asks me to explain it, then I don't know what it".
Warm regards, Harv