Can i go out and return from the right country ? and my two children? What if I take them out of the country and the return?

Your question refers to the "right country," however that concept does not exist in US immigration law.

Can a new employer transfer my visa and can file PERM for me when I'm out of USA.

This is possible. Consult with an immigration attorney to discuss the specific requirements and timing issues.

When can we file I-751 (got married in March 2014) and husband obtained green card in October 2014??

Between July 2016 and October 2016. Pay attention to the actual date of approval.

My question is. Does those facts mean that my case is on a good way? is it going to be accepted?

The case is proceeding in a normal fashion. Whether it would ultimately be approved is an entirely different question.

What should I do?

You could hire an attorney to file a lawsuit seeking a Writ of Mandamus from the US District Court to compel USCIS action.

Will my work for the UN in Iraq be counted as residency in the US ?

You would need to file a Form N-471 with the USCIS in advance.

Question related to stay in US

You would be subject to the 6-year limit, even if USCIS has made a mistake on your I-94. Consult with an attorney before making any firm plans.

You will not need a new PERM as long as the job opportunity remains.

TPS: Do I have to maintain a valid status/visa while in temporary protected status

No, you do not necessarily have to maintain nonimmigrant status.

Is I-140 considered as an "Immigrant Visa Petition" or just an "Immigrant Petition"?

technically, it sis called a "Petition for Immigrant Worker," which is an immigrant visa petition type.