I agree with my colleagues. There is the issue of possible visa fraud. It is best to consult an attorney to evaluate your options.

Should i file a petition for a hearing on naturalization or to request a write of mandamus or calling to senator/congressmen ?

You may want to contact your Congress member. 5 months is not a very long time, but background checks can take time.

45 days is not a long time to wait. If you do not hear anything after 90 days you should make an infopass appointment.

Can my cousin sponser me to Green Card

No your cousin cannot sponsor you.

When the case was complted and all the preprocessings was completed,and nvc told me that they told more when they schdul intrviw

Only the NVC can tell you when an interview will be scheduled. Cases in Pakistan do tend to take a long time for an interview because of security...

I made a mistake in my VAWA affidavit, I wrote my son's name instead of my husbands name. And later my son's name is mentioned .

I agree with my colleague. You should consult your attorney. It is usually best to correct mistakes in an affidavit.

Immigration: I-131 filing with I-130/I-485: is 30 days 'expected length of trip' reasonable?

Yes it is reasonable, but you may miss your interview date. You also need to be in status as an I-131 by itself does not guarantee you will be...

Will my fiance be able to stay In the U.S. even if we have a child here?

It does not sound like he qualifies for Deferred Action, but it is best to consult an attorney. If you are a US citizen, marrying your fiance...

I have a tourist visa, I have traveled several times to the U.S., my last trip was 2 years ago

You will need a lot of proof that you will only be staying one week starting with a round trip ticket.

H-1B to B2, now want to change of status from B2 to H4

You should be okay. A B2 is only allowed to have the intent to return to one's home country whereas a H4 is a dual intent visa. Consult an...