My parents got their green card 3 yrs ago through my brother who is a US citizen. When can my parents apply for US citizenship .

They can apply within 90 days prior to the 5 year anniversary of becoming Lawful Permanent Residents

F1 OPT EAD Case outside normal processing time

You should be able to speak to a live person by calling, you are just probably pushing the wrong numbers. Question is whether that live person...

It is just a category under which you received your green card. There are many different categories out there. You do not lose it upon divorce.

What step should be taken by out of status F1 student married to Greencard holder with 2 kids?

As far as adjustment of status - she can't do it, until her husband becomes a citizen. As far as F-1 reinstatement - depends, need to know more...

What is I-485 response time?

Be patient and give it a little time. Sometimes I receive a receipt notice within 2-3 weeks, sometimes, it take a bit longer. Patience.

How should I proceed in filing a new Deferred Action case?

There is no appeal for these cases, but you can re-apply using new evidence and an attorney on your side.

Immigration status of daughter

Your daughter does need to go through the process of adjustment of status.

My mother is trying to fix her immigration papers so she hired this lady, she said she had connection with ice so she Said pay

Have your mother speak with a licensed and reputable immigration attorney as soon as possible.

If your visa is still valid and you have not violated it in any way, then after the asylum officer denies your case, you go back to that status and...

N-400 application document requirement for spousal death certificate. Is it really critical?

Yes, you need to submit proof of termination of all marriages. The death certificate is such proof in your particular case.