Will it affect the water pressure if a 3/4" meter is installed on a 1 1/2" water line?
Putting any obstruction or turn in a water line will affect the flow and hence the water pressure. Not only will narrowing the line cut the pressure, but all the meter-related crap inside the device will cause massive turbulence and other flow-restricting effects.

As far as legal issues are concerned, read whatever agreement you may have signed with the district.

Note that state laws always trump any bullshit local regulations, so read state law carefully. In my experience, local administrators often do things that are ridiculously illegal under state law. Often you can coerce such pint-sized local despots by finding some violation of state law they are making and threatening to complain about to the AG or to sue them outright for it.

Water is always very political. In many cases your best course of action is to gather a large group of people (like all your neighbors) and storm city hall. This will often frighten the local gauleiters into stop doing whatever it is they are doing.