Yes. An SSL Certificate will cover the domain name and all folders/files within that domain. So if you choose the domain to be "secure.mydoamin.com" then anything transferred on there will be secure.
If you are using multiple subdomains, then you would possibly need a wildcard cert, but other than that a standard SSL Certificate will cover your needs.
As above, an SSL certificate will cover everything on the subdomain.
Just make sure that you don't, for example, register the certificate for a particular subdomain, thinking that it can be used on all other subdomains and the main domain.
Hi!
It is important to note that many Certs do not include a prefix "www" along with the base domain. I would not consider buying a cert that did not include this.