Are quality scores independent for every AD, or will one ad getting a good quality score influence the ad position of other ADS within the same adgroup?
Quality Scores are determined at the keyword level only. However, generally speaking, every aspect of your account does impact its history and performance. A bad performing ad is likely to pull the account's performance down since it affects the accounts history.
Actually, QS is calculated at the ad-keyword level. It is shown only at the keyword level but there's a different one for each ad and keyword combination. See Adwords FAQ.