Can I file a 1098-T for College Tuition I paid for a daughter who is a NON-Dependent? She is a dependent of my ex-wife but I pay 60% of her College tuition.

No.   You can only get an education credit for yourself, your spouse or for a dependent who is claimed on your tax return.  Actually---if your ex-spouse claims her as a dependent then she can use the education credit on her return.

No. Whoever claims the student as a dependent is the only one who can claim expenses for the credits and deductions.

You are not able to claim any education credits for a non-dependent child. To be able to claim education credit, the student in question must be a dependent claimed as an exemption on your tax return.

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Since the ex-wife claims the student as a dependent, she can claim the tuition credit and count the money you paid, in calculating that credit,  in addition to anything she and the student paid.