Suppose I buy a house and sell it off in the same year for the same price, would the GDP for that year increase by twice the value of the house, or only once, or not at all?
There is only a change in GDP to the extent there are market goods and services used in the sale and only those goods and services are counted. The actual sales revenue are irrelevant. For example, the home inspection, appraisal, brokerage fees, and, I believe mortgage closing costs, would be in GDP. If you and your sister swapped houses in as-is condition without getting the market, bank, or tax authority involved, there would be no change in GDP.
Not directly, but if you paid for the house by taking on new mortgage you would create additional money to be spend by the seller.
Imagine before the sale you had $10k savings and both you seller earned and spend nothing more or less than the year before; GDP in this year would not be affected if you haven't exchanged the house.
Now if you took 90k mortgage and handed 100k to the seller you would have kept your income/spending the same so you would not increase GDP. BUT seller would now have new $100k to spend and if he/she spends all of it GDP would boom.