My site has a wildcard ssl certificate that will cost a lot to renew.
I believe “Full” encryption will suffice, So I hope to avoid this cost.
1 Will this work correctly even though the domain has multiple A and CNAME records?
2 If so what steps do I need to take, if any, when the existing certificate expires?
No. If you’re expecting a secure connection to your server, you’ll not get that with anything less than Strict.
The article @sandro linked to includes solutions to maintain a secure connection, such as the Origin CA certificate. You can do this right now, before your expensive certificate expires.
It won’t be less secure, it won’t be secure at all, because you won’t have any validation whatsoever.
So your entire hypothesis is wrong, which makes the whole question pointless I am afraid.
I am not sure what you mean by “this connect”, but nothing will change in your setup, except that you will have an insecure setup at that point, which anybody can take over as outlined in the article. But the HTTP connection itself will work - of course on an insecure setup.
Full (non-strict) allows expired and self-signed certificates. That’s the essential difference between strict & non-strict: strict requires that the certificate is signed by a CA, and that it’s not expired.
1 Will the CF DNS continue to work even though the domain has multiple A and CNAME records?
2 If so what steps do I need to take, if I decide that I am OK with the security issues incurred by using the Full setting, when the existing certificate expires?
Cloudflare’s DNS system is unrelated to any encryption mode. You can switch it to Off and it will still work.
There are no steps to take here. Get any valid certificate, such as an Origin certificate and make sure it is correctly configured on your server. That’s a matter of a couple of minutes.
You can get a free certificate from Let’s Encrypt. You could also get a free origin certificate from Cloudflare. There’s no real reason to pay for certificates any more.