I've heard of instances where a buyer negotiated with lien holders to pay off a reduced amount of the debts upon settlement.

Two years ago, we had guest slip-and-fall at one of our clients' properties with a $250K settlement. 

Are there signs of settlement on the rest of the house?

Also, would there be two sets of settlement costs that need to be accounted for in the deal?

In your case a "Delayed Settlement" would not work, that is the problem in the first place. 

In order for the title company/escrow to prepare the ALTA Settlement Statement, which you will sign at closing, they will have to have received the closing instructions from the buyer's lender.

The Virginia Bureau of Insurance put an end to split settlements back in February.

All other things being equal, having a nice rapport with the seller can mean having a 120 day settlement term rather than 5, greater flexibility to inspect, or show the property and countless other details that can make or break your deal.

Also very common for basements is settlement cracks in foundation walls (concrete cracks, this is normal).

If anything, I'd bring my issue up with the seller directly and look to come to a settlement outside of court.