About Sign E1 and E2: parking ban or standing-still ban: which statement is WRONG?

With sign E1, you may also no longer stand still to load/unload or let a passenger in/out.

It is exactly the reverse. Sign E1 (one diagonal stripe) = parking ban: standing still for loading/unloading or getting in/out is still allowed. Sign E2 (two crossed stripes, a cross) = standing-still ban: that forbids EVERYTHING, including loading/unloading.

'these signs only apply to the side of the road where they stand'. The opposite side can have a completely different situation.

With E2 'you may not stand still afterwards (and therefore not park either)' — with no exception for loading/unloading.