Best way to add external power supply when main PSU is a solar charge controller? I have a 12V 20A Solar Charge Controller (which is part of my existing Solar Panel System Setup connected to a 12V Sealed Lead Acid Battery) that I will use to power up some pumps with the help of relays and some sensors. And because its a solar charge controller, the output varies depending on the sun, from 12.1v to 13.8v (I set the Load Reconnect, Load Disconnect, Float Charge etc which technically 12V to 13.8V)
How do I power my Arduino Mega safely in this case?
I am planning on using a separate buck converter that will give my Arduino a fixed 9V from the Solar Charge Controller.
Should I power the Arduino with the buck converter parallel to the same PSU (the 12V 20A Solar Charge Controller) I'm using for the pumps and is it safe that way?
or
Should I use a 9V battery to separately power the Arduino Mega?  and what is the explanation behind the concept of using an external PSU for the Arduino Mega when the total Amperes all in all is not exceeding the limit 20A at all?
Should I power the Arduino with the buck converter parallel to the same PSU (the 12V 20A Solar Charge Controller) I'm using for the pumps

Yes. However I wouldn't use a 9V buck regulator, but a 5V one and feed it to the 5V pin. That way you bypass the wasteful LDO on the Arduino, and when running from solar every bit of power saving you can muster helps.

and is it safe that way?

Yes, it's safe. As long as the buck regulator you are using is rated for the voltages in question.