If a man has a daughter with a woman and then many years later, he divorces the woman, does his daughter become halal for him to marry?
It's forbidden; the Qur'an is clear on this:
Prohibited to you [for marriage] are ... your daughters ... and your step-daughters under your guardianship [born] of your wives unto whom you have gone in. -- Qur'an 4:23
She remains his daughter after divorce, and the father retains his rights and responsibilities as a father ("at all times, the father of the child is responsible for maintaining the child" -- Mufti Muhammad ibn Adam).
The Qur'an even goes further to forbid marrying step-daughters (see above).