Hostname / local domain name questions

I'm newer to fortigates and was setting up ssl certs which got me wondering about the device hostname and a few related questions.  I see the field in the settings page to define the hostname. 

(1) Should that hostname be the full fqdn that would resolve to the firewall device and match my ssl cert or should it just be the name without the .contoso.com part?

(2) should the local domain name field in the DNS section match the internal domain, the external domain, or I see it can have multiple, so should I do any/all internal/external ones we have?

(3) I have a cluster setup (not sure yet A/P or A/A)...  the cluster has a name.  should that be a fqdn as well?