Is CloudFlare compatible with a website with SSL?

Yes, a site with SSL can use CloudFlare, however there is an extra step. If the SSL is on its own sub-domain, then ensure that this sub-domain is marked with a gray cloud. If the SSL is on www, then you have to upgrade to a paid service (either Basic or Pro) and follow the directions here.

Are there domains that shouldn't be enabled with CloudFlare?

An orange cloud means that your web traffic will pass through the CloudFlare system making your site Faster, Safer and Smarter. A gray cloud means that your traffic will not pass through the CloudFlare system.

Only CNAME records have the option to be powered by CloudFlare, meaning that only CNAME records have the option of an orange cloud. However, not all CNAME records are appropriate to pass through the CloudFlare system.

To decide which records pass through the CloudFlare network, you need to understand what type of content appears on that subdomain. You should enable CloudFlare for any subdomain that gets web traffic. You should not enable CloudFlare for subdomains that handle non-web traffic, such as mail, FTP, and ssh. These types of records should be marked by a gray cloud.