Visiting the US on vacation with an open Green card application?

They can try, but because of the pending immigrant visa petitions they will most likely be denied

Someone I know married an illegal person and he has never lived with her only paid her rent, now he has quit doing that and quit

She can contact Homeland Security at (866) 347-2423 or http://www.ice.gov/exec/forms/hsi-tips/tips.asp

What would be the cost to make my brother resident in the united states?

The filing fee to the government is $420.00. Attorney's fees vary. You can petition for him if you are a US citizen but the wait time is quite...

Can I lose my green card if I get a divorce after 7 months of marriage?

Yes you may. You can apply for a waiver of the requirement to file a joint petition to remove conditions on residence, either on good faith...

I got my H1B visa stamped on 15th March 2013.Now if I apply for F1 and its rejected, will my H1B visa Revoked? I dint travel yet

I agree with my colleagues

My children are already US citizens with US passports. What form should I file to get a certificate of citizenship for them?

You do not need the certificate to prove their status. Why do you want it? Is there a particular reason?

Change of Status from H1B to L2 Visa

Yes you may. Contact your husband's lawyer to ensure nothing goes wrong.

Can you file for Green Card through work, if you have a pending application for Green card through US Citizen siste?

You can have more than one visa petition pending at the same time.

From your description the visa has not been cancelled.

Am I eligible for Cap Gap?

You should consult with an attorney