Ok there are a few changes you need to make to the BDE MSM to get it to work properly:
Open the MSM in Orca or Inst Ed
The errors requiring admin rights when your user self-repairs all come from a dodgy CustomAction.
Fixing the CustomAction's Component:
1. Go to the Component Table. Find the TempFolderFiles row. Delete the values in the ComponentId and KeyPath columns.
Fixing the CustomAction's Condition:
2. Go to the ModuleInstallExecuteSequence Table. Find the BDEConfig Row and set its Condition to "Privileged".
This really is a poor MSM.
While you are in the ModuleInstallExecuteSequence you should fix the condition on BDEReduceUseCount. It should be the same as BDEBumpUseCount, changing the 3s to 2s.