You won't be able to run all of those things. 12Ah is not a lot of energy. My Jebao dct-6000 return pumps uses 50W, so a 12Ah battery could run the pump at full speed for just under 3 hours. However, battery performance is imperfect and you would get less run time.
The nice thing about the DC pumps is that you can slow them down to increase run time. However, those gains would be partially offset by the need for an inverter to convert the DC to AC to run the control unit.
If it were me, I would focus on a setup that keeps pumps and an air pump running in the event of a power outage.
That's not quite right.
Your pump is taking AC, and converting it to DC. The draw on the system is 50w/110-120v - or .416amps
If you have an inverter (takes DC and converts it to AC), then a 12ah battery could power that pump for ~28 hours (ideal - 20-24 is probable)
The issue is that cheap inverters don't put out a true sine wave. It's modified, and modified sine waves can put a strain on electronics if used for extended periods of time.
I have 8 12v-18ah AGM lead acid batteries (very high quality) hooked up in parallel and connected to one of
these.
It's an inverter and UPS, so it senses when it loses AC power and kicks on the batteries. It also charges the batteries when on AC power.
That gives me 144ah. My system's full draw is around 4 amps when the heater isn't on, and 6-7 when it kicks on. That would give me 36+ hours of battery backup if I ran everything.
I only have my return pump, wave makers, heater, and dosers hooked up to the battery backup, so I have 3+ days of battery power in the event of an outage.
If those batteries are in decent condition and haven't been cycled a ton, they can definitely be used to cobble together a battery backup system that would give you a good amount of run time in a power outage.