DS-260 Form

The fact that it has been reopened means they are looking at it again. You should not have to re-file.

Why the I-485 request for my wife and my 3 kids is taking very long time. Does traveling affect?

The travel does not affect her ability to adjust status unless she travels to her country of nationality.

I wanted to know if its better for them to file for her or if I should try and file for her. Which process is easier and better?

The processes are different. Your parents can get their residency rather quickly because they are in the Immediate relative of a US citizen...

What shall I do now

You can call again or make an InfoPass appointment. Look on the USCIS website.

What is the best way for me to get to the US?

At present there is no best way for a Syrian with your circumstances to get to the United States. You can certainly apply for a J-1 residency...

If I become a citizen of another country (ARG) would cause me trouble getting my green card or after years residing US citizen?

Getting citizenship in another country will not hurt your chances to get approved for residency in the United States.

Can I work for 5 years on my J1 visa?

The maximum length of time you can stay in the US on your J visa depends on the program you are involved with. Medical residents have the longest...

You must file a separate petition for each family member you plan on sponsoring because you are a US citizen. So file three separate applications...

Is it okay for us to fill out an i-130 and send under the current situation?

You can adjust status under section 245(I) if you meet all the requirements. The I-130 visa also had to be approvable when filed. As you appear...

Can Hong Kong based company file for P3 USA visa for Malaysia based speaker for a show to be hosted in the USA ?

It is possible but the first step is to hire an attorney experienced in these matters to assist.