1. I call this a bad question. We normally say "very hot indeed", but "hot indeed" is simply uncommon.
2. It's not a passive sentence, so "dead" (adjective) is correct. Also, "to die" can't exist in passive form.
3. "Quite" is not possible here. It's a very vague word for describing degree, so only "a lot more interesting" makes sense.
4. "A bit of a fool" is the only correct option. The other expression we use is "a bit foolish" (ie. "foolish" being an adjective).