'Of ill repute' refers to a bad reputation, and yes, absolutely it can be harmful, regardless of the truth.
Noxious
That is not a word. The actual word would be unsuitable. It means inappropriate.
That it's bad and can hurt you.
She was a prostitute. She worked in a house of ill-repute. ill repute = bad reputation
It's just a way of saying "I'll tell you why" used by certain regions.