I'm going to take a stab at this. Hope I don't get too complex even though the question is really several questions.

Glacial ice is mostly the result of past snowfall. Ice is what you get when you compact the snow and get rid of all the open space. It is pretty much the same idea as the conversion of mud into rock. The snow undergoes metamorphism in a away, it recrystallizes from pressure (weight) perhaps with some melting, flow of water down into open space, refreezing, as well.

As you know, we live on a seasonal planet. The result is that there is seasonality in precipitation and temperature. These variations cause ice to form distinct layers for each year, very much like how tree rings form and the thickness of the rings reflects what went on with the weather during that year. Some rings (some layers) can be fairly thick, and some are almost non-existent depending on what happened over the course of the year. Dry year, not much snow=thin layer.

Loose snow can be 80-90 percent air, or to put it another way, you get about 10 inches of snow for 1 inch of rain. The conversion is ballpark, not precise. I am sure you have heard something along those lines, and the point being made is that water, liquid water, has a density of about 1 (g per cubic centimeter) but snow has a density of about 0.1. Only 10 percent. When converted to ice, the ice will have a density slightly less than water (why ice floats in water).

So, you lose about 90 percent of the volume even if no melting or sublimation (evaporation but without passing through a liquid state, from solid to vapor directly). Apparently about half that density change from snow to ice happens in the first year. (makes stuff called firn, snow from previous winters that has not converted into solid ice) and the rest happens over several years or more.

That is how we go from snow to glacier. How much snow? Well, that really varies a lot. Some places will only see maybe a meter of snow per year, and other places maybe 10 meters or more, with most places having permanently winter conditions getting something in between.

Lots of places still see some above-freezing or near freezing temperatures so sunlight heats the snow to melting, during part of the year (like say on high mountains) so part of the snowpack gets lost by melting and evaporation/sublimation. So in many regions, the amount of original snowfall that makes it down into ice might only be a small percent of the original, perhaps 10-20 percent. So, if we started with a meter of snow per year, we might only get about 5 cm of ice. Still, even at that slow rate, you could get 5 meters in a century and 500 meters in 10,000 years.

So, how fast does it accumulate? You can get some pretty important changes to ice extent and thickness over the period of a millennium (1,000 years), even when there is not a lot of snowfall, but generally it will be slower even if there is a lot of snow (because of loss through evaporation/sublimation and melt runoff).

Many thousands of years is generally needed to make a good glacier and tens of thousands of years to make an ice sheet (massive glacier). Some ice sheets, like in Greenland, have been drilled and cores removed, going back 100,000 years, and even further back, several hundred thousand years, in the Antarctica ice sheet.

Africa has largely missed on continental glaciation because it is too close to the equator, or too far from the poles. Mountain glaciers and flow onto nearby lowlands is indicated, but no massive ice sheets. Same idea with Australia. South America had a pretty well-glaciated spine almost up to the equator (the Andes mountains are so high that glaciers could be formed even near the equator), but much of the continent did not get glacial cover.

Two reasons why the northern hemisphere got a lot more glacial cover than the southern hemisphere: 1) the Arctic is an ocean so lots of moisture can be transferred to nearby land, and 2) a lot more land in the northern hemisphere is near and in the polar regions than in the southern hemisphere.

The ice sheets in the northern hemisphere mostly never got further south than about 45 degrees N. Most of Australia, Africa, and SOuth America, is further north than 45 degrees south. Basically southern lands a lot further from the south pole than northern lands from the north pole. Apart from Antarctica, of course. Frozen pretty solid down there.