I read the "Move a domain between Cloudflare accounts
" - but I didn’t really understand… so I have to remove the site and open it as a new one in another account? There is no way I can do the transfer without taking down my site?
Are you talking about an external domain (registered elsewhere but using Cloudflare nameservers) or one registered via Cloudflare Registrar?
If you are talking about an external domain, you can simply create the zone in the new account, make all the necessary settings and then change your nameservers when you are ready.
This would usually not cause more than a few seconds of downtime.
If I understood you correctly - an external domain, so I need to open it as a new one? The last time I had about 24 hours my site was down, that’s why I’m asking…
What does connecting to cloudflare really give me, on the free account?
Yes, just add the domain to the account that you want it in and make sure to copy all the necessary configuration from your old account (DNS records, SSL settings, rules…).
There is really no reason why your site should experience more than a few seconds, at most minutes, of downtime.
There’s a lot, but the biggest features on the free plan are Cache and Firewall in my opinion.