Can I file 'writ of mandamus' for business visa?

People have done this.

Can I work on H1B after COS filed?

No, not until it is approved.

I'm illegal for 20 years, want to return to my home country in EU. No passport (it's expired). Can I use state issued DL?

This is a website for immigration to the U.S. If you want information how to get admitted to your country overseas, you may wish to contact your...

How can I stop a deportation for my wife that she still breast-feeding our 6 months new baby?

We are missing a great deal of information. Without meeting in person and getting all of the facts there is no way to answer this. But briefing,...

How long will it take for the USCIS to make a desicion?

There is no set time. Follow up after 90 days.

Can you travel within the USA with an unexpired passport after your deportation case have been administrative closed ?

You seem not to have any way to get admitted back into the U.S.

Filed the I130 petition in 2004 for husband he was deported in 2008 can a new petition be filed

Yes, you can file for him after he spends 10 years outside the U.S., or more, depending on why he was deported in 2004.

I-130 approval what next ?

They will get an email from the National Visa Center, with further instructions. It will be at least 3 - 6 months before you can immigrate.

I am currently in H4 and applied for H1b.My Petition is still in initial review but My H4 is getting expired in Nov 2013

If you do that, you are asking USCIS not to give you an H1b, but rather to keep your H4. If that's what you want, you should withdraw your H1b...

Your priority date does not depend on what status you have in the U.S., or if you leave the U.S.