Yes a separate power supply needs it's own battery. Battery size is not just based on load but also runtime. Calculating it based on the documentation is not going to be reliable, you're best bet is to test runtime by pulling the plug and seeing how long it lasts.
Nope. Not true, that method is a good way to plan on system failure and not performing to spec.
Calculation for runtime is going to be figured out on total load with all the devices in alarm state. Plug in some numbers, then figure on the current draw. I'd work up the values and multipliers, but I'm working on another problem elsewhere. Also, as the batteries age, temperature and cyclic use, a lot of times you're not going to see the rated output of the battery at the panel.
The best way to go about it, even with multiple supplies, is to treat each item as their own entity and NOT install a massive 55 aH battery and hope for the best, spread across 2 or 3 separate supplies and the panel itself. Good way to burn equipment up and have long charge times after a power loss/draw down. If you were going this route, you might as well install a large UPS and then 7aH batteries to take up the slack on the UPS and act as a buffer on the panel for overload.
Size each supply's battery appropriately with the panel having the longest standby. Also plan on using 0V loss power supplies for expanders, as Elk isn't too tolerant if the voltage starts to drift below 12, modules start to reboot. Many power supplies don't advertise the voltage loss when running on DC only, typically a volt or even more, from the battery voltage.