You can check your site is on google search box by putting your full URL, If you don’t find your site or any of inner page of your site then you may consider it as banned.
The other easy way to check the same - You can use mention tool to get the information about you site whether it is banned or not.
This is completely untrue. There are several reasons for a site not to appear in Google’s index. Just because it’s not in the index doesn’t mean it’s been banned.
In fact, very few sites are banned by Google. Even sites that break Google’s guidelines, and even those in which Google detects malware, still appear in the index.
Google does not banned any site but the rank of site may down. Google rank site on the basis of Content used on the site. Google Crawler index the pages of your site. They take a snapshot of the site webpage. Ranking are affected by Penguin and Panda(Google’s Algorithms to improve search). Keep your site updated with unique contents.