Hello. My name is ***** ***** I will be assisting you today.
The product key is tied to the mother board, HP should have fixed this when they replaced the motherboard.
If you have recovery discs then yest reinstalling it will fix the issue.
You answered Question 1. What about 2 and 3?
It takes up to 90 minutes I would say.
I've never had an issue reloading a PC with recovery CDs, odds are very very low.