Do the sub-domains inherit (are protected) under the main site that has https (SSL security)?
I have a new domain and am going to have a few sub-domains under it. If I configure the main domain as a HTTPS will the sub-domains automatically be protected?
Subdomains are not protected by same SSL as another domain (unless you're using a special SSL like a "wildcard" SSL). If you're using the standard Free SSL we offer through your account management panel, subdomains will automatically be assigned their own SSL. However, sub-directories (like example.com/directory/) of any protected domain will be protected because they are beneath the protected domain.