Do I petition for my wife and step-child at the time?

Yes you can file and yes only the I-130 at Service Center and the stepchild will process at US Embassy in their country.

Travelling on Advanced Parole?

You are assuming you will get the AP by August. If you do then you should be fine. You will be returning as a pending Adjustment of Status...

You have 2 options 1. Wait while continuing to make inquiries or 2. Hire a lawyer to file a mandamus action in Federal Court.

What can I do?

You are allowed to stay past L status expiration date while waiting for I-485 adjudication.

Can i?

You ate not getting a green card solely because of medical condition. You can apply forna tourist visa to get treatment.

How to divorce in nyc deported husband married for 2 months in nov 2014 iand he was deported jan 2015

This is not an immigration question but a divorce question. You can do a divorxe by publication if you cant find him. Consult a matrimonial lawyer.

When can step-child petition be filed?

Did you marry husband prior to child’s 18th birthday?

N400 Naturalization

You also have to look at the amount of days outside the US on any trip and in the aggregate to see if you qualify.

Make an infopass appt and go into local office and inquire as to status of case.

How?

Have him contact the consulate general of his country here in the US and apply for a passport to use to get married.