Two part question:
1. How can a customer remotely change a greeting, or re-record a greeting? Is it possible via DTMF? Inclement Weather related question from customer.

2. I would like to be able to get remote admin via manager to systems installed. Fairly new to Avaya. Have lots of experience with Samsung systems. Seems that we should be able to this with port forwarding?

You will see the codes for recording greetings in the auto attendant, such as 7841 for the Menu Options of AA1.
Check the box for Dial by Direct Number, and set selector code 7 to Dial by Number. You should be able to reach the AA and dial the code 7841 to re-record it remotely.

There is also an Emergency Greeting, 7861 for AA1, and you can set a selector code to "Transfer to Emergency Greeting" to enable remotely.

Not so much for Basic mode, but if you have a PC on site, load Manager on it and use TeamViewer or LogMeIn to access remotely.

Otherwise, be VERY careful to port forward the relevant ports and whitelist ONLY your IP that you will be remotely programming from.

Thanks for the help!