Why does FEMA require separate flood policies on each structure?
You need to ask FEMA. My guess primarily for the purpose of obtaining additional premiums to fund the NFIP.
Help me understand what seems to be silly red-tape, in my opinion.
Quite simply - it's the law. Yes, the flood requirements are a law.
Is the Lender the only one responsible for ordering the determination properly? Or is the Flood Determination Agency responsible for completing the determinations in compliance with the regulation?
The lender is 100% responsible for the accuracy of the SFHDF, including the determination whether the property is in or out of a SFHA.
What happens if you only have one determination with multiple buildings? Is the property ineligible for insurance?
If the multiple buildings are on the same property (parcel) then one determination is sufficient. If the multiple buildings are on separate parcels then they are on adjacent properties and you must have a SFHDF for each adjacent property.
The failure to obtain a proper SFHDF would not make the property ineligible for insurance. You would just have to correct your error and then obtain the insurance.