Would it be possible to produce a non-toxic atmosphere using a coal fire and frozen oxygen?
Yes, it is possible to produce a non-toxic atmosphere using a coal fire and frozen oxygen.

I'll answer your questions last to first. 

No, low pressure oxygen will not make flammability worse, fires require something to bond with oxygen (often carbon, causing carbon dioxide). Low pressure will make things less flammable as there is less oxygen to bond with.

Yes, using an open coal fire in a semi-enclosed space will gain toxic levels of carbon dioxide, carbon monoxide and sulfur dioxide (among a few others) quickly. However with a minor modification from a open fire to a fire in a old fashioned chimney pipe stove (venting outside the hut) would eliminate this.

Lastly, Definitely Yes, a coal fire will produce more than enough energy to thaw the oxygen it uses. To quote figures 1 pound of coal will produce roughly 12,500 btu's (British Thermal Units) Assuming the temperature of the frozen oxygen we are thawing is -455°F (the "temperature of deep space") and about 3 degrees below the freezing temperature of helium. To thaw 1 gallon of the frozen oxygen will require roughly 900 btu's (if your stove has a 80% efficiency) and produce 860 gallons of pure oxygen at 80°F and atmospheric pressure. Coal will consume 140% of it's weight in pure oxygen, so for 1 pound of coal 135 gallons of your oxygen will be consumed. Leaving you with 11,500 btu's extra heat and 725 gallons of oxygen. The average Human consumes 25 gallons of oxygen per day making this plenty to survive on.