Would the certificate for "www.example.com" protect "example.com" (and vice versa)?
Would "www.subdomain.example.com" protect "subdomain.example.com" as well?
For a single domain: Yes, both domains would be protected. Same for subdomain cases.
Doesn't matter if insert the common name with "www" or without "www", both versions appear in the certificate. After the certificate delivered the Certificate Authorities automatically include "domainname.com" or "www.domainname.com" as an additional name in the certificate.
For multidomain: No, include both www and non-www domains in the list of domains.
In case you add a wildcard (*.domain.com) in the multidomain order, the www. is considered a subdomain so this is covered by the wildcard domain. Check this article how to order a wildcard in a multidomain ssl.