Married filling separately. Your spouse isn’t eligible for the benefits of MFJ as you’re a non-resident alien for tax purposes. She could also file as head of household if you two have kids.
Yes - you will need an ITIN as you’re a nonresident alien.
You’re an exempt individual and a nonresident alien for tax purposes under the terms of the NATO visa. The United States Government hasn’t seen you “entered” the United States for tax purposes so any substantial presence tests don’t apply to you as your days in the USA don’t count thus far until you get a new visa type that isn’t designated for foreign government officials. The US requires you maintain your tax home in your foreign country under the terms of the visa.
You will still be subject to US income taxes for some US sourced employment, some passive US sourced income will be taxed by the US, and any gains on sales of US real estate. You will file Form 1040 NR to report these gains in the future years. Become familiar with the US tax treaty between your country to understand when certain US income will be subject to taxation back in your home country as a foreign government official any notes exchanged between the US and your home country.