It's complicated and professional help (maybe even a tax attorney) may be warranted.
Although you have effectively inherited half a house, it's not clear if that's what legally happened. If your father retained a right to live there ("life estate") when he put you brother in the deed, it is usually treated as inherited. if you are a named testamentary beneficiary of the will, it would support that position.
Assuming it qualifies as inherited:
Q. Can I deduct any improvements made to the house by my father?
A. No. The cost basis, in an inherited property is the fair market value on the date of death (your cost basis would be half that), not you father's cost basis, as in the case of a gift.
Q. Can I deduct closing costs from the profit I made?
A. Yes. With the stepped up cost basis, you may even have a loss. You may deduct the loss, if the property is treated as investment property instead of personal use property. It is personal use property if you, or any family member used it as a residence after your father died.
