How do I check out that this domain has not been blocked or check what history it has?
I'm not sure how you check the history of the domain. (Maybe do a site:domain search on Google and see what that throws up?) If it has been blocked by Google in the past, that shouldn't be too big an issue. Once you have the domain on-line with your own content, submit a reconsideration request through Google Webmaster Tools, explaining this is a new site under a new owner and that should remove any penalty.