I installed that inverter last year; I don't have the mate so I can't answer your first question.
I have the oem Port 32v batt bank connected to the Outback. I don't know the AH rating of the batteries. The PO installed them and I cannot read the sticker on the side of the batts because the box obscures it. Although I'd like to know the AH rating, I am not interested enough to actually lift a batt out of the box just to read it!

I can say for certain that they are generic 8v wet cell batts - they are certainly not Rolls/Surettes!
My system is not wired to assume all a/c loads. I have a relay that switches some of the a/c circuits from shore/genny to the inverter. So I have to turn on the inverter (remote switch on the panel at the top of the galley stairs) and flip the switch that changes over the circuits (in the same panel). With the 3232 I could automate this but the circuits were installed back when the original inverter was installed by Hatteras of Lauderdale in 1980. It works fine so I didn't/don't see any reason to change it. This made the Outback inverter a simple "drop-in, hook up the same wires, we're done" installaton.
The circuits that are switchable are the fridge, wall socket at the microwave, wall socket at the starboard aft portion of the salon (stereo/tv), starboard wall socket in the master stateroom above the shelf (tv and shelf fan). I have had the boat out of the water for 36 hours with the fridge running the entire time. I have had the boat at anchor, inverter only, for approximately 24 hours with the fridge, tv, a fan, and the microwave operating at "normal" intervals during that period. In both cases, the batt bank started the port engine with no hesitation.
This is not a lot of load but the performance of the batts/inverter exceeded my expectations. As a result, we have no need for additional batts for the inverter. Obviously if you wanted to add a hair dryer or any other heavy-draw equipment running for more than a very brief period, more batt capacity would probably be necessary.