Power and motor advice requested - wall power to 1 arduino and 1 vex motor

This project is a single VEX 2-wire motor 269 (with motor controller 29) signalled by 2 PIR sensors that open 2 small swing doors when the puppies get close. Brains is the arduino UNO r3

Trying to determine the best way to power it.

When turned on I need it to operate 24/7, so wall power with adapter seems to be the way to go, so I would like to be able to run all of this from one power source. I have the arduino powering the sensors directly, the problem occurs when adding the motor.

While I have used the arduino a decent amount in the past, I have never dealt with motors so I may be overthinking this and the answer is obvious:

Everything I have read says power the motor separately, but all the examples I have found are a) battery and b) multiple motors.

STATS
1 VEX Motor Controller 29 : MAX 8.5V - MAX 4 Amp
1 VEX 2 Wire Motor 269: 7.2V - MAX 2.6 Amp (stall) / 0.18 A (free)
1 Arduino Uno + 2 PIR sensors: 5V - sensors run at less that 60 micro amps in idle state

I have a 12VDC 8.5A wall power switcher from a previous project but I think that would be overpowered?

Looking for advice on how to power this:
a) -can- this be done from a singular power source as the mechanism is stationary and mains power based (I know I can't run the motors from the arduino and thinking to split the power, ie in parallel)

b) I have read that while an arduino can take 12V, it can not deal with with it 24/7 due to heat buildup but that was disputed by a few people as well,. Anyone have practical experience on this?

c) will my 12VDC 8.5A wall power switcher work (with resistors for the motor to bring it down to 7.2 or less) or is it just too much? If too much what should I be looking for in a wall adapter?

This is where my lack of motor knowledge comes into play, does a motor controller take power and use it for itself and the motor or is the motor an additional load on top of the controller? On the motor, I don't need speed (in fact slower is better) but I do need a bit of torque as the doors have a spring close. Looking for V/A requirements to be looking for in an adapter if that is the recommended way to go.

You may get by with your adapter, but it will be close. The efficiency of your buck converter will have a big impact on this. You can use a buck converter to generate the 8.5V for the motor, this will be adjustable giving you "torque" control. Then use a smaller buck converter to again create something in the 8-9 volt range to power the Arduino via Vin. Reason that will give you additional power filtering on the supply. The sensors can be powered via the Arduino +5V pin. You can control the motor (bidirectional I think) with a BTS7960 bridge, not very expensive. If it is only single direction you can use a opto isolated MOSFET switch available for a few dollars from your favorite china supplier. This should get you going let us know how you do.

Thank you so much for the answer, and thank you very much for the whys. So much easier to learn when you know why you need to make the suggested changes!

Sub-note in case anyone else is looking for this info: I forgot to put this information and and gilshultz mentioned the different options. Motor is bi-directional. It will wind up 8-12 inches of cord to open the doors, hold and then unwind to let the doors close normally. Using vex motor controller 29 to talk to the motor with the arduino h.servo include.

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