Unless you bleed the pop off valve when filling the water heater the first time, you have what amounts to an expansion tank already in the system. There will be air trapped in the top of the heater as it fills - and there's nothing wrong with that in my book. It give the water a place to go as it warms up...
Regarding this VS pump style and expansion tanks, because this pump reads line pressure to vary pump speed, it might be possible for the expansion tank to cause the pump to surge a little. Not a big deal either, but that's just an opinion.
Regarding checking voltage at the pump, to get a true picture of what's going on there, that check should be done with the pump running. Otherwise, you would get the same reading with tiny wire, or something the size of battery cables. As long as the circuit is complete, there will be voltage.
What we need, is wire big enough to allow for enough amperage to keep the motor from overheating. The only way you can measure that with a voltmeter, is with the motor running. If you see the voltage dropping significantly as the motor kicks on, you have reason to doubt the wire size has the ability to handle the necessary amperage.
Under ideal conditions (fresh batteries, or while plugged in), the voltmeter should show something close to 12v (minimum) with the motor running....
1997 37' HR Endeavor, 275hp Cat, Freightliner
03 CR-V Blue Ox, Ready Brake