What you can generally do is delegate a subdomain to different nameservers (which would be NS records for “dev”), however you cant add dev itself to Cloudflare, at least not on the lower plans.
yes, you can do that.
just add a period after the domain when adding it.
I’m using it myself.
Yes, if you are an enterprise customer we support that configuration. and it can be enabled by your account team. Not supported today on self serve plans.