Am I eligible to apply for green card since my aunt (Mom's sister) is a US citizen.

Your Aunt is not permitted to file for a green card on your behalf.

Can a family friend who is a 1 person household sign Affidavid of Support?

It is possible for the friend to file an affidavit of support.

Can the sponsor and the petitioner show on their I-864 different years of tax returns?

You can file only one year, 2014, or more if you wish, unti April 18, 2016 when taxes for 2015 are due. Years do not have to be the same.

Will immigration have a problem if we file tax separately?

Joint tax returns are an indication of the commingling of a marriage. But if there are other good supporting evidence of a good faith marriage, not...

How long does the process take to file for citizenship, my green card expires in August 2016

The process can take about six months to complete application, biometrics, and finally the appointment. Oath can add additional time.

Can I ask for a political asylum, by reason of oppression on a workplace based on my nationality?

Unfortunately, your situation is not one of the enumerated reasons permitted for asylum. If the reason for your "oppression" would be deemed as say...

Renew EAD (granted from asylum) while I-485 is still pending.

Without a valid EAD, you are not authorized to work. The timing of approvals are never certain, especially in asylum cases, so it is probably best...

For immigration purposes, expungement does not make the conviction of a crime go away.

Can my cousin who is a US citizen give me a green card?

No, there is no provision in the law for cousins to petition for cousins.

Will that affect her status are permanent resident?Can she still apply for I-131 after she leaves USA.

I-131 must be filed from the US. It cannot be filed from abroad. Caution should be observed that the green card is not abandoned due to excessive...