Can i be denied my citizenship if i have 2 different birth certificates from 2 different countries?

You need to consult with a Board Certified Immigration attorney immediately. You cannot assist for this on a blog.

Can a foreign born mother married to a U.S. citizen with two U.S. born children leave the U.S. without their fathers consent?

No, they cannot. That is kidnapping and you could be in serious criminal jeopardy.

Your question is very confusing but you can probably use her passport if she never obtained a certificate of citizenship.

You cannot "change status" outside the US. You can only get a visa outside the US and it is highly recommended you do that in your home country,...

Need to know current status - EAD/ AP card received in August 2017.

It looks like you are stuck in background checks. But it is difficult to determine that since we don't have enough information.

I have filed I-485 In February 2017, I was granted asylum 2 years ago and received EAD. Should I now pay I-765 fee to renew EAD

You do not have to pay the I-765 filing fee.

If you travel now you will invoke at least the three-year bar and probably the ten-year bar based on these facts. You can travel once your receive...

Can I get a J1 visa or any other visa after my visitor visa was cancelled? The immigrant officer demanded me immisable?

You have to get a waiver if you want a visa before the five years expire. The waiver must be based on hardship to a parent, spouse or child who is...

Will I be allowed to come back to USA from South Korea with my new I-20 and old VISA?

Normally you need a new visa but check with ISSO at TAMU and they will clarify this for you.

You can only cross charge based on a spouse's nativity, not based on parents'.