Is there a special din regarding taking challah for lechem mishneh to be used on Shabbat? Can one use simple pitas for lechem mishneh even if challah was not taken. Are the halachot it different from other days of the year? If challah is not taken from something, may the bread be eaten nonetheless?

There are no special rules of lechem mishne. No bread may be eaten if it was baked by a Jew, had the requisite amount of flour, and challah was not taken.