I am going to add my take in the form of a questions rather than a statements of fact (but I believe to be true). First, the certain factors you mentioned are that the points charged for the original mortgage are deductible in the year the mortgage originated up to the sum of cash paid by the seller and buyer. It doesn't matter what the cash was put up for. It could be for the down payment for example.
Second, the costs of obtaining the original mortgage, appraisal, inspections, title fees and so on, are included in the basis for the property.
