Am I right in thinking that all shooting at chargers is completed before any charges are moved?

It's been suggested to me that for each charge you complete the shoot-evade-charge sequence for one charge before attending to the next charge, with the consequence that some shooting can be nullified if someone gets charged from the flank before they get a chance to shoot frontally.

You are correct.  All shooting at chargers is completed before any charges are moved.  This seems pretty clear in the rules to me.