Hi!

I've connected the 1100AH to the normal power (230V) and connected Eth13 to a POE injector. If I removed one of the two power connections the Mikrotik kept running. Has this setup any bad side effects?

Is there a possibility to monitor if one of the 2 "power supplies" goes down?

You can use such a setup.
But ensure, that you don't switch too often between internal and external power during operation, because this might make RouterOS crash.
The internal Power supply is 12V.
I recommend 24V PoE powering.

This way the RB1100 will use PoE powering (cause it always uses the source with more voltage).
If the PoE-powering fails, you'll notice a voltage drop in /system health from 24v to 12v.
Unfortunately you cannot monitor the failure of the internal power supply.

So effectively, this allows for a 'dual power supply' set-up that is known not to burn the board ?

Is this dual power-supply setup possible with all Routerboards that accept power through both PoE and a Power port and don't use a jumper to identify power source? For example, RB751s and RB493s?

Dave

to my knowledge you can dual-power all boards.
These boards have diodes built-in to separate the power.