Hi there and welcome!
First up, the extensions are hardcoded with the Partner systems. 12 will always be 12, there isn't a way to change the extensions. This is just by nature of most of these sorts of more analog key systems. If you want this ability, you'll have to step up to a full blown PBX, like an Avaya IP Office or something like that.
To administer from your PC with an R6, you'll need a modem (looks like the CF29 you have had the option for an inbuilt modem),
this software from Avaya, and that's about it. To administer the Partner Messaging module, you will need to connect the LAN port on the Partner Messaging to a network, set the IP address using the serial interface (needs a specific pinout adapter, if you need it let me know), and
this software for the Partner Messaging admin. The Partner Messaging will work over data networks and does not need the modem.
To get into the PACS R6 modem you'll have to plug your modem in to any extension port and open the admin software. Then use that to dial extension 76 which is the inbuilt modem. That will connect your to the PACS and let the system download the configuration. This will take a while and can pretty easily fail. If you run into difficulty, turn the speed of your computer's modem WAY down and it should work, albeit even slower.
Unfortunately working with systems this old, these are the sorts of things you'll have to deal with. But on the flip side the Partner ACS is still a great system to set up and use, and with the onslaught of licensing and subscriptions, will probably outlast most of the newer more advanced systems.