When you serve your website through CloudFlare, their servers take care of (and control over) all HTTP connections. As such, they can enable features like Keep-Alive, even when your web host does not support it. Now that you disabled CloudFlare, connections are handled directly by your web host, and apparently they have indeed disabled keep-alive.
I’m assuming you are on shared hosting; in that case, there’s not much you can do about this. If, however, you are on your own VPS or dedicated server, you can enable keep-alive via your web server’s configuration files.
It looks like you’re not allowing your pages (i.e. your HTML) to be cached, which is fine (and often makes sense) for dynamic content, but it also means that when you serve your website through CloudFlare, their edge servers will always have to forward the page request to your web host, rather than serving it directly as they would with cached resources such as images, thus adding a bit of processing and latency. This might explain the slightly higher TTFB.
You can always ask your web host, of course. In some rare cases, you may be able to turn it on via .htaccess, but most hosts simply prefer to keep it off to avoid having too many active connections on the server (which can be costly).