Is there no distinction between 'warm' and 'hot' in Norwegian?
Yes. Varm(t) = warm, kjempevarm(t) = VERY warm (in other words, HOT).
is the word "sauna" not common as substitute for "badstua"?
They're both common.
Isn't the 'd' in badstua silent? I can recall an explanation like that in my norskkurs, but i could hear the audio pronounce it quite distinctly.
Yes, I would leave the 'd' out when pronouncing it.
I said, "Det er varmt i badestua," but it said it was wrong, and that saunaen is correct.
Because 'varmt' means 'warm' not 'hot'. The 'kjempe' added to 'varmt' changes it from 'warm' to 'VERY warm', ie 'hot' ;)