Make sure you've disabled Windows Firewall, any Antivirus software with intrusion blocking (such as Norton). Also try asking someone to portscan you to see if anything is being blocked.
Connecting to a server over LAN is the same as over the Internet except you should use local addresses instead...the ports will remain as whatever you set them to be.
Run MTAClient.exe and connect to a server. Tadaa, you can see the chat!
You can also see it in game in the top left corner, press T to type in there and then Enter to send your message..
You generally can't do script commands through remote admin. Why would you want to anyway?
Never going to happen in this version, and probably not any versions in the near future.