I'm filing dual status (left US permanently in March 2006). Both spouse and I are Irish, I have two children, one a New Zealand citizen, one a US citizen.
1) I can't claim them as exemptions. Correct?
2) Can I claim Child tax credit for my US citizen child?
2b) If yes to Q2, how? Do I enter her details in line 7c of 1040NR and not claim exemption and just use that entry as documentation of her SSN?
Any help appreciated.

1) No, you CAN claim them, but only against the income earned in the U.S. from 1 Jan 06 to whenever you left in March.

2) Same as #1, only for the time in the U.S.