If you have legally established German residency, then you do not have to remain registered as a "resident" of NY - just cancel your NY voter registration and identify yoursel f as a resident of a "Foreign or U.S. Possession" in the Personal Info interview of TurboTax.
Unless you renounce your U.S. citizenship, however, you continue to be subject to U.S. tax.
If you are filing as "married filing separately", your wife's salary (for U.S. tax purposes) is zero ("0") and her dependents are also zero ("0"). They want to make sure that you aren't double-claiming dependents or misallocating family income. Since she is not filing a U.S. return and does not have any U.S. income, that is not an issue.
The only way you can properly identify her as a Non-Resident Alien (NRA), is to use a paper return and file by mail.
If there is no ITIN or SSN, then in any place where the nonresident spouse's taxpayer ID number is required on a tax form, you would take a black or blue pen and manually write "nonresident alien" or abbreviate as "NRA." In the TurboTax software, you can input any "made up" SSN or ITIN you want to, in order get through the program (we suggest 999-88-9999, 999-88-9998 or 999-88-9987, as those numbers won’t produce any TurboTax program errors in a review check) as a temporary "placeholder.” You can then later "white out" that number when the paper pages are printed.
