If you have not deducted the home improvements as lease expenses during the period that it was rented out and you did not depreciate those improvements then you can add the amounts that you spent to your basis in the home when you sell it. Be certain that you did not already deduct those amounts.
If you had not already deducted those amounts they add to the basis on the home. The basis is what you paid for the house. That and any selling expenses are deducted from the sale price when figuring what your profit on the sale is. Your profit is what you will be taxed on. So yes, they will be deducted before figuring the taxes due.
Yes. Purchasing another home with the proceeds has no effect on the taxes due from the sale unless you are doing a 1031 exchange which requires that you use a 1031 exchange professional to hold the money for you prior to the purchase.
Here is some information on 1031 exchanges.
@Am076
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