It slowly turns to ice, compressed by its own weight.

Thereby enabling us to get https://en.wikipedia.org/wiki/Ice_core and analyse the layers like tree rings, err... https://en.wikipedia.org/wiki/Dendrochronology

It accumulates on top, turns into ice, but the bottom layers of the ice very gradually flows (tenth of thousandth of years) toward the see. Modeling that precisely is hard and we do not know if Antarctic as the whole gains ice or looses it.

My current understanding of the numbers is that the East Antarctic Ice Sheet (which includes the South Pole) is in positive ice mass balance, while the West Antarctic Ice Sheet is losing ice mass and is in or near a complete collapse scenario. It seems that the eastern sheet isn't gaining enough mass to offset the loss of the western sheet, but every study seems to contradict the previous study so... :shrug:

That depends who you mean by "we", but for people who follow this stuff the GRACE measurements are pretty clear.

In short: they become glaciers. The snow gets compacted into ice, which then slowly moves as a glacier (motion is highest at the base, I think) until it eventually reaches the glacial margin.