Hi
Auction position is based on how your ad ranks in like an auction that will deternime what position your ad will show on the page. Auction position is like a rating of your ad which decides its rank that determines where to place it on the page based on that rank; 1st, 2nd, 3rd, etc. or even which page to place it on, 1st page, 2nd page, etc.
Rank of your ads depends on quality score which is based on factors I'm not all too sure of totally, but I do know that it does includes relevancy of keywords to your ad and relevancy to the users' search queriies, and your bid.
I think ad preview is part of the Ad Preview and Diagnosis Tool you use to see an example of your ad on the page without being on the real page which could contribute to lower quality score by increasing the number of impressions without increasing the number of clicks on your ad.