What are the consequences of incorrect positioning of air separator (and swapped return/flow) in solar heating system?
Having the coil connections crossed over will decrease the efficiency of system.  In the worst case it would be better to turn off the solar part of the system than have it run as installed!

In a heat exchanger like this, you want the outgoing fluid to be as cold as possible.  For this reason you want it exiting the bottom of the tank where the water is colder.

In your case it might be so bad that hot water tank is heating the fluid above the input temperature and that the solar system is actually removing heat from the hot water tank.  Even if it's not that bad it's definitely not good.

For more information look into counter-flow heat exchangers.

I don't know what would cause the pressure drop but I would agree with you that it appears your air separate was not installed as per the manual.