Two questions (local network and system logs)

[Man Alive]

Hello all,

I am setting up a local mail network with no outside connection, just
users on local network emailing each other - can postfix be set up to
do this? I have no registered domain name, so how do I define
domain/host/origin? I have had trouble finding website that explains
how to set up an unconnected mail network with no registered domain
names. If you could explain how to set up these names (a sample
configuration) or point me to the website that helps me to set it up,
I would appreciate it very much.

Secondly, what is the best way to mail all system logs to root mailbox
before they are rotated? Are there any ports that can do that? Or
if better, which is recommended - using "crontab -e" or setting up a
shell script? Again, either website or sample configuration/script
would help me tremendously.

Best regards,

Jonas