Can i leave US while my Asylum case is pending?

You should have no issues leaving the USA.

If they are immediate family, he should apply for them now based on his LPr status.

How long does a detainee have to hire an attorney in NJ before ICE deports them?

What are you waiting for? Hire an attorney now. He may be able to get bonded out and be with his family.

Is it possible to renew my greencard normaly or i dont have possiblity anymore? Since it has passed long time since i had it.

No, you will have to start over with the green card process. It is only for Legal Permanent Residents, not for those that want to live abroad.

Filled my N-400 as single while married by mistake?

You may want to correct it. This could have a big effect on your wife's potential immigration later on.

My aunt(mother's cousin) is a US Citizen, can she sponsor GC for me or my mother.

No, only immediate family can sponsor family green cards, not cousins.

How do I get my father his lawful permanent residence?

You can apply for his green card as his adult son. Once he has the green card, he will not need the EAD any longer.

How can I solve this: Married in two countries, having a green card?

This is a messy situation. You need to hire a competent divorce lawyer and Immigration lawyer.

Can USCIS sent two EAD with one bearing wrong receipt number?

I am not clear on what you are asking. They received and EAD for the I-360, what is the problem?

Sponsor

Yes, another US citizen can be the sponsor.