Would I qualify for residency?

No the facts in your question do not permit you to file for residency.

Can I still go through the process of getting a green card if my husband is on probation?

Not living together is problematic in proving a good faith marriage. But hopefully you have put together a package of proof far beyond that.

Can i File petition for my mother ?

Yes you can based on the facts submitted.

How can i stop the process of my spouse getting her green card.

Withdraw your I-130 petition and affidavit of support. May want to visit with family attorney as well.

How do I make a correction the last name in green card?

It depends which is wrong. If it is the green card file I-90. If you are not at fault you don't pay the fee. If by name on travel you mean your...

Am I still enligible to apply for a green card after I divorced with my husband?

Once divorced you lose the opportunity to start the process. However, you may want to look at qualifying for VAWA if marital abuse was present. I...

Is there any way to faster the IOM or SIV case,

The IOM is a program designed to assist in displacement of Iraq nationals. The SIV program is approved annually effective October 1 each year with...

I am on adjustment of status i already did the biometrics and i still waiting for auhorization of employment and green card.

The idea of maintaining a correct address at all times is to insure you revive all communications from immigration and can then properly respond....

No it would not be okay. You have applied for immigrant status for your family by filing the I130. A visitor visa contradicts that.

Can my 19 year old step daughter, who is in the US with visitor visa, adjust status (I-485_ based on her mother's pending I-485

No derivative for your wife in this instance so step daughter will need her own I-130 and I-485.