You need to change the name servers for your domain to those provided by Cloudflare. From here you can delegate sub zones to other nameservers as long as they don’t expect the same configuration. I guess Google does.
This won’t work. As far as Cloudflare’s DNS servers go, www isn’t where the zone cut is. DNS resolution will be weird and unreliable. And eventually Cloudflare will delete the domain because it’s seemingly inactive.
if you’re on the business or enterprise plans, you can use a CNAME setup.