is google looking to the new sub domain as new site even if the other sub domain in the same domain is BLACK HAT WAY !
yes, subdomain1.domain.com - different subdomain2.domain.com - different subdomain1.domain.com/something - not different. ( blogger would have been banned years ago)
Yes! subdomain.example.com and example.com will considered as two different websites. one has nothing with the performance of another. There are millions of websites on wordpress.com and blogspot.com. and most of the website are being promoted via black hat or grey hat techniques. but that doesn't mean that Google will penalize the wordpress.com or blogspot.com. only the specific sub-domains will be penalized. But make sure main domain and sub-domains are not extensively linked with each other.
Subdomains are usually treated as two different sites (not exactly though as of common IP) and if one subdomain is blacklisted then it may effect the other as well because blacklisting is done on IP or main domain level.