darkmatter to answer your questions:
Q: When changing filters, does the focuser automatically adjust?
A: not automatically but you have to to turn it on with the flip of a switch
Q: Is the focus position offset for each filter determined in advance, or is the V-curve run every time the filter position changes?
A: you can opt-in to autofocus when changing filters. Again it’s a flip of a switch.
Q: Is focuser backlash taken into account?
A: according to a reply from ZWO on this forum, set backlash to 0 and ASIair Pro will handle it by itself. I leave it up to you to find it by yourself.
Q: Is focus checked periodically to account for thermal changes or atmospheric diffraction?
A: yes, there are options the autofocus at changes for 1, 2 and if i remember correctly 5 degrees Celsius. Again it’s a flip of a switch.
You will find all those settings and some more in the EAF setting window under advanced settings
.