CERTAINLY Danko, in post#13, has presented what I consider an effective circuit to provide the functionality described in post #1.
If very accurate current readings would be required then adding regulation to the supply for the op-amp and offset divider may be required.

This is what is most feared, besides shorts, spikes and reverse mishaps on the output. Do you have any suggestions for the most precise and rugged and stable supply for 5 V in 150 to 300 mA output range?

 

The setup is suppose to be able to distinguish hopefully down to at least 10mA current flow in both directions. Dont think a hall can do that?

You are correct, hall sensors are used to sense much larger currents. They might be capable though, but would have to read the full data sheet to validate that assumption.

 

WHICH POWER SUPPLIES WILL BE AVAILABLE at a reasonable price, and what quality will be available, depends also on what part of the world you are in. Availability varies widely!!

 

WHICH POWER SUPPLIES WILL BE AVAILABLE at a reasonable price, and what quality will be available, depends also on what part of the world you are in. Availability varies widely!!

Usually using Digikey or Mouse. Am in Denmark.

 

OK, those are both honest suppliers with true specifications listing.
And usingav separate supply will avoid damage if the battery connection gets reversed. So there is an added value in that aspect.