Connection order to controller

[crotalus]

Should one connect the controller to the battery first than the panel or the other way around? Or does it make any difference?

And why?

[inetdog]

Should one connect the controller to the battery first than the panel or the other way around? Or does it make any difference?

And why?

It makes a lot of difference for some charge controllers, not so much for a smaller number.
Most CCs instructions tell you to connect to the battery first before applying any PV voltage to the panel input(s).
For some this is necessary to detect what battery voltage is being used before trying to send any charging current into the battery bank.
For others it is necessary to properly power up the processor and initialize the operating system firmware.
In either of those case if you apply power to the panel input first they may freeze with an error indication or they may just not work properly and give you no indication why.
A few allow you to apply panel voltage first. I do not know of any that require the the panels be connected and producing power before the battery connection is made.

[crotalus]

What should one do if the battery needs to be disconnected/replaced? Disconnect the panels first?

[inetdog]

What should one do if the battery needs to be disconnected/replaced? Disconnect the panels first?

Technically you may not need to disconnect the panels before disconnecting the battery. But you must have the panels disconnected before you reconnect the new battery.
There should be a DC disconnect in the panel circuit.
Or replace the batteries at night.