If you have not purchased a SSL certificate for your domain, then SSL is not going to work correctly.

The whole point of SSL is to identify your site, and to reduce the chances that someone can intercept communications with your site. Without that cert, these things don't make sense.

If your host is clueless, get a different host.

As for CloudFlare, if they don't support SSL, it's likely for a reason. Perhaps their concern is being able to faithfully transmit communications from the browser to them and then to your site. I don't know. You could ask them.

In any case, typically, SSL is only needed for a small portion of a site, say, at the point where personal data and/or credit card information is being transmitted. CloudFlare helps optimize portions of your site which have heavy traffic. So why not partition off the areas that actually need SSL, and let the rest get optimized?

Who's the host?

1- You are using a shared ssl cert on your domain and that is yourwebhost server ssl cert

2- Have you purchased dedicated IP? you need a dedicated IP address for SSL. as ssl encrypts the information it could be the reason
for not supporting it. often cache servers and traffic filters do not work with ssl, because ssl encrypts and do not go under the cache server.

Using SSL currently requires upgrading to a paid plan for SSL to work properly, if the SSL is on the root domain or www.

We will, however, move to making SSL free later this year.

You need to understand how the tech works.
SSL is https, which is not the same as a "normal" website (http).
It's not a simple matter of adding an 'S' on the URL.
Those are technically two different sites. (And yes, you can run two sites, one http and one https!)

Some of your confusion comes from trying to oversimplify things.

Stablehost is an excellent host, with knowledgeable people. So rather than ask for something, and then think they're stupid when you get confusede -- listen to them! If it's confusing, ask more questions. They're an extremely newbie-friendly host, which you apparently are right now. That's fine, you'll learn, and they don't mind teaching you.

Inversely, you may say something confusing to them, not knowing correct jargon/terms. So again, rather than think they're stupid, explain yourself again in another way.

It sounds like CloudFlare is attempting to access an https:// on the IP, as opposed to http://site. Right now, I'd contact CloudFlare for clarification on what's going on, not the host. Not yet anyway.