Your past should not be an issue. However, at the permanent resident stage of the processing, you may also need DOS permission to file for a visa.

Green card Recd in May 2018. LUD update text received for i485 in Jan 2019 but no status change ?

I find this confusing - what green cards did you get?

Newborn before I-130 approved. How to add derivative?

Not a problem. The baby will be added at the Consulate/Embassy stage of the green card process.

What is the likelihood of a reduction on an 1180a ticket?

This doesn't appear to be an immigration-related question.

Can we apply only EAD under C9 Category for Dependent Kid based on pending AOS under C9 Category . Kid only has AP only now.

If the child's AOS is pending, you can file the I-765 with a copy of the fee receipt.

I485 and appeal and warning about a deportation order ?

Schedule a consultation with an immigration lawyer of your choice.

Do I have to go to the interview with my mom from New york to California for green card since I'm the citizen?

In some jurisdictions, the petitioner is expected to show. Your lawyer advised you that this is the case in California. We are not your lawyer,...

Is better a cr1 visa ?

The American need will need a legal marriage certificate if he is to file for you to come live with him here in the U.S. Did he file for you already?

Should I request a service center transfer for I-130 application, since the CSC does not work with US citizen - child case?

CIS alone decides where and when it has available manpower to get the job done. I have had cases where the parent petitioner/naturalized after...

IR2 visa filed by my step father.

You could expect questions about you and what you have been doing with your life: are you the sort of person they would want to let into the U.S.