Let's say I buy a website which last owner used his adsense on it or might be used it to open his account, and after I buy I use it to apply my new account.
Absolutely. Google works the other way around: Account contains Sites, not Sites contain Accounts. I have a friend who runs his AdSense on some of my old sites. Never a problem.
Yes, you can apply with a site that has used AdSense on another account, provided you remove the other account's ads (of course). Google doesn't care which account a site uses, as long as the site fits their requirements. You don't even need to change the site's WHOIS info - I have a friend who opened his AdSense account using one of my old sites (which I had run ads on before) and now runs his ads on it. The site still belongs to me. Simple answer to your question is "Yes".
Yes you can; BUT almost a few times each week the Google adsense help group is get complainats from people who purchased sites that previously had adsense; and then applied for adsense using the site they purchased and got declined. The site may have previously had adsense on it, but it was probably not the site that was used to get that previous owners adsense account approved .... so due diligence is important.
Well, I think the answer has been already provided, You can apply a new account using your website but you should remove Google Adsense codes from it. And you need to make sure that the site still comply with Google Adsense before applying.