I think you have a handle on it. Item #2 applies to the student. If the STUDENT is filing MFS, then the STUDENT can not claim the education credits. It is important that for the two of you, the student does not take the self-exemption OR the exemption for you (since she has to put your SSN on her tax return). The same holds true for you too. While you the non-student will take the self-exemption, make sure you do not take the exemption for her, since you have to include her SSN on your tax return.
Finally, since you two are filing MFS, understand that if one of you itemizes deductions, then you both MUST itemize deductions. Even if that means the itemized deductions for one of you adds up to zero. This is why the IRS requires the spouses SSN on an MFS return - they use it to confirm you both itemized, or you both took the standard deduction.
