Yes, USCIS recognizes legal marriages, even if you don’t live together as long as it’s a real marriage and not just for immigration.

 You’ll need to provide strong evidence that your relationship is real: messages, calls, photos, financial ties, visits, joint plans, etc.

 If you're still emotionally and financially connected, and you can prove that, you still have a strong case.

Yes, a legal court marriage is valid for immigration even if you’re not living together.