You are correct. "than he" is correct, "than him" is not correct. This is a common misconception in English. https://www.grammar-monster.com/lessons/than_I_me_than_he_him.htm
'Literally zero results' is a well-placed piece of journalese. I'll have to check with my American friends whether draws worse is part of their common parlance. For me, 'draws worse' doesn't work in written UK English. I'd better return to struggling with Polish. Thanks and best wishes - stay safe and keep well.
Not according to this British dictionary. Like I said, it's also an adverb so the Duolingo sentence is grammatically correct.
The examples given in the dictionary are in common English usage but I don't think that applies to 'draws worse' even if it were to be grammatically correct. It's not polished English - but as I already have polished English I shall just continue to fulfil my aspiration of acquiring polished Polish.