Cloudflare via hosting partner, help me understand the set-up and how I can improve it + SSL Concerns

I have a couple of websites with an Italian shared hosting company, and they are Cloudflare partners.
They have set up all their domains with Cloudflare, but I’m struggling to find out what kind of set-up it is, and the hosting company cannot provide me with individual website access to the Cloudflare dash.

When I test the domains with Selesti, I get they both use the Cloudflare DNS, Proxy and SSL.

But the DNS records in DirectAdmin for the domains are still pointing to the hosting servers.

Is the hosting <-> Cloudflare link on a higher level, in this case?

If I wanted to obtain more control, how would I go about migrating my websites from the hosting’s partner account to my individual account? Do I simply add them to my dash and configure the DNS myself? Or should I go through Cloudflare’s support?
The hosting company explicitly said to contact Cloudflare support for this, but I just wanted to ask the community first.

On another (maybe related) note, I have two more doubts regarding the Cloudflare SSL set-up via the hosting provider for these websites:

  1. When I test the SSL protocol via SSL Labs, I obtain a “Grade B” score; this seems to be because the certificate is set to support TLS 1.0. Would this be a setting that my hosting can switch if required?
  2. I have the following error in the Apache logs of both websites:
Thu Apr 23 00:11:06.071846 2020] [ssl:warn] [pid xxxxx:tid xxxxxxxxxxxxxxx] AH01909: www.domain.com:443:0 server certificate does NOT include an ID which matches the server name

Is this to do with Cloudflare, with my hosting provider, or otherwise with what? My hosting says that it’s an error due to Cloudflare but I shouldn’t worry about it :thinking: :rotating_light:

Thank you!

First, if you post your actual domain name, we can better evaluate the situation.
Second, I’m not a fan of partner setups because of limited access to core features.

It sounds like you’ve got the right idea. You’ll need to disable the Cloudflare integration at your host, then add those domains to your regular Cloudflare account. Then you can do things like set minimum TLS.

Do answer the DNS question, your DNS records won’t change, as Cloudflare needs to know your host’s IP address. The public won’t see it, though.

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