Retirement tax questions

No. The improvements add to the value of the house and are not eligible for the penalty exclusion.  However, specific dollars are not tracked -- it doesn't matter if the withdrawal is used for the improvements and then you use other cash for the closing as long as the money you provide to close (deposit, down payment, other closing costs) are equal or more than the amount you withdraw from the IRA.  And there is a $10,000 max on the penalty exclusion.