If the bank receives the insurance proceeds first, are they obligated to apply those funds toward repair/reconstruction, or can they choose to reduce/settle the mortgage debt instead?

If the bank receives the insurance proceeds first, are they obligated to apply those funds toward repair/reconstruction, or can they choose to reduce/settle the mortgage debt instead? 

This depends on the terms of your mortgage agreement.  There may or may not be any obligations on the bank to use the insurance monies towards repairs.  If there are no obligations, then the bank can decide how it uses the insurance monies including whether to reduce / settle the mortgage debt.