I clearly did not think of this when opining that I'd change both sides for uniformity. My bad.

 

Calipers do not need to be replaced in pairs.
Rotors, those I'd replace in pairs.
Pads I'd normally do in pairs as well but since the OP's "old" pads only have 1000 miles on them there's really no need to dump them.
They do need to be bled well. I can see where air in a line could cause uneven force between rotors.

 

Pretty sure since everything past the MC is common, the pressure while poor if air is present, will be the same everywhere.
Get the air out.

 

For a two rotor front the line splits out of the mc to go to each rotor. My 07 Ultra splits the lines under the lower steering bearing. If one caliper was replaced it's entirely possible there could be air in only one line. Would that not cause one calioer, the one without air bubbles, to exert more pressure than the one with air? It seems logical to me.
I do agree that all the air needs to be removed.

 

The line pressure is equal everywhere at any given lever position even if it is low pressure because of having compressible air anywhere in the system

 

Absolutely, whether it is mushy because of the air or perfectly bled and firm, the pressure is equal.
NO - doesn't matter where the air is, or how many lines, the pressure is distributed the same throughout.

 

The new thicker pads will contact the rotor stronger than the worn pads. Thus the rotor will be warmer.