I heard that MOZ or DA is important in search engine ranking. So, if I buy a domain from Godaddy auctions, will the MOZ score reset to 0?
It will not reset. It is based on external factors. The thing that may change is the backlinks may drop as other sites realize that the link is broken. I don't know if MOZ has published the details of what their exact criteria, but I would image that losing it's internal linking structure while its down may cause the DA/PA numbers to drop, possibly a lot.
The page/domain authority is a metric started by Moz (similar to Google's PageRank). This collected data is intended to predict how well a website will rank on search engines. Since that's only something calculated by Moz, the search engines do not consider it for their ranking system. However, a domain with a high authority will usually be a domain with good content, high-quality backlinks, social shares and so on. Therefore, it's very likely to rank well in the results of the search engines as well, without having a direct connection with the domain authority measured by Moz. If you buy a domain which already has a good authority, that should remain after you buy it. Still, keep in mind that this score can also drop after some time if the domain doesn't receive backlinks, it's content is not shared on social networks, and so on.
Moz counts links with own robots and those stats are not correct. I have a website that shows DA 40 and PA 62 and counts 13.000 links. Googles webmaster tools shows over 45.000 links so you can see how correct are those informations. Btw, only links wont rank you. There are over 30 key factors for ranking on google and one of them is time.