Identifying peat bog: don't know an official way but sphagnum moss (and associated stuff) on top is a likely indicator. You can stick your hand right down into it and come up with a sort of compost-like soggy mass, deep brown or black, that is peat. It is all quite soft and usually mushy, unless you go at the end of a prolonged dry spell.

Grow-back; not significantly, cuttings done many years ago will have got a bit of vegetation regrowth, but peat accumulation is a process taking hundreds of years to form a depth worth talking about.

How deep? I have seen beds cut to well over a man's height, I don't know if there is a record, though I would expect so.

In some communities peat cutting is a right, with particular families having traditionally cut particular stretches, not necessarily on their own land. Little peat in now hand cut, though there is certainly still some in both Scotland and Ireland. Much of the early mechanical cutting was either for horticultural use, or for power generation.

Can't really describe the smell of peat burning, it is just an aroma that you are unlikely to forget. A nice one.

Peat is often burned just on a stone or concrete slab. It smoulders and glows mostly, not a lot of flame. A firebasket or a stove can be used, but isn't a requirement. Briquettes seem to be targeted at the more sophisticated arrangements, if you have a stove it would be worth checking its suitability with the manufacturers before using peat.

Size of pieces cut varies a bit, housebrick size is pretty common, or a bit bigger. Different densities will dry differentially, and locals will have found what works best locally.

Briquettes have a sort of slightly waxy finish, but if you break into one the nearest equivalent texture I can think of would be a coarse form of MDF board.

I don't know about Alaska, but those conditions sound possible, is it warm enough to get sphagnum growing, I wonder?

Commercial peat exploitation is something the green lobby are fighting quite hard for a number of reasons. It is still going on in the UK and Ireland, though I think that the environmentalists are gaining ground. There used to be quite an industry in Germany (Peat-Bog Soldiers, anyone) but I don't know whether that is still the case.

One word of warning; old peat cuttings are a first class place for doing yourself a mischief. You will end up at least filthy and knackered if you spend any time there, and there is always the possibility of serious injury.