Welcome to the Forums @Matt93094
I use the following Transformer without issues with my Doorbell Duo:
This is what the Duo Doorbell Tech Specs says:
AC (10-24V AC, 60 HZ)
and this is the SD Card sizing:
Local Storage: Supports up to 256 GB microSD in exFAT format
EDIT
To answer your other questions, you know if it is hardwired by a plug symbol over the battery. This is what mine looks like:
