1. Basically, the books have been masterfully building up to/foreshadowing Dany potentially going insane in a slow, believable way and becoming like her father. Unfortunately, the TV show writers didn't have the nuance or the patience to do that so instead they threw it together quickly at the end. The result is that it does feel illogical and unearned.
2. Personally I don't have an issue with that, I assume the dragon is breathing fire with a huge amount of power so that combined with the heat is probably going to do a lot of damage to the (fairly primitive) architecture of King's Landing.