I am a non resident alien. Can I file state taxes married filing separately with my wife--even if she doesn't have a social security number nor ITIN?
Is she required to apply for ITIN?

If you file "married filing seperately" you do not file "with your wife."

Generally, aliens must always use the MFS tax tables.

I am a non resident alien. Can I file state taxes married filing separately with my wife--even if she doesn't have a social security number nor ITIN?
Is she required to apply for ITIN?

If you are nonresident alien (as you have stated), file nonresident tax return.