There is not much of a difference between Request for Initial Evidence and Request for Additional Evidence. You still need to provide the...

Do i have to put the country of residence of my parents?

Yes, you have to provide all the answers to the questions provided truthfully and to the best of your ability.

Green card interview went well but no decison made on the spot

If there was no major issues that arose during your interview, you shouldn't have anything to worry about and you just have to wait.

Yes, it is possible to apply for H1B while your I-485 is pending because H1B visas are dual intent visas. That means that an H-1b application can...

Should I say I was unemployed during that time or admit that I was a Nanny?

You should be truthful in all immigration questions. In addition, you should not knowingly omit any pertinent information.

Is their any action to take against them? how can I protect my status through this? should I complain to SEVIS/Homeland Security

I believe that you may need to consult with an experienced and qualified immigration attorney to thoroughly go over the facts of your case.

Should i change my name now? How do i change my name?

You could change your name but it could result in delay of your mother's application. You can petition for a name change in your local state court.

As I have valid H1B stamping on my passport, still I have to appear for visa interview at US Consulate?

No - Generally, a person with a valid visa stamp in their passport does not need to apply for a new visa stamp.

H1B COS F1 COS back to H1B visa status

I agree with my colleague but is there something specific that you wanted to ask besides the resources that he gave you?

Is getting visa easier for Iranian applicants after nuclear deal and prisoner swaps? or just as same as before,,,

I think that it is the same if not more difficult.