Is it bad to replace nuvaring every three weeks without leaving it out for a week?

No it is not bad. This is perfectly safe and can be used to diminish the number of periods that you have. There is the risk of spotting and breakthrough bleeding at times, but overall it is a safe option.
Yes. But there is more than 28 days of medicine in each ring so you can safely change it every 4 weeks and still skip your cycle.