@alyle99 

So is the sales price and cost $307,803?

No, the sales price and basis before selling costs are $337,000.  The sales price should match the amount reported to IRS on the 1099-S.

None of the other items would be added to the basis?

Selling costs are added to basis.  

By effect distribution does that mean that since there were multiple heirs the house was sold so the asset could be distributed?

Yes.