Can a U.S. citizen sponsor parents?

Is your sister over 21? if so, she can petition for her parents (meaning your parents). It sounds like your parents may able to adjust their status...

Green card holder applying for wife.

I agree. There is no minimum. Your co-sponsor should be a USC or LPR. For income of your co-sponsor, please see I-864P.

What is the procedure to file for U Non Immigrant status when a Waiver of Inadmissability is required?

If you can't afford an attorney, try to get a list of legal clinic near you. The waiver form is I-192. I really wish you good luck.

Could my 601 waiver be aproved?

I agree with my colleagues. Hire an immigration attorney near you.

What kind of visa should i apply for to be able to work in the uk without sponsorship?

You should consult with an immigration attorney there (UK).

If I get an E2 in the US (with legal status in the US). Do I still need to coordinate with the US embassy in my resident country

If you want E2 visa, you may want to coordinate with the US Embassy. If you want to change your status in the United States to E2 status, you don't...

We are overstayed am I'm working since 2004. Will these affect our family based petition from my US citizen daughter?

You will able to adjust status (thus get the green card) as a Parent of United States Citizen int he United States.

My question was that how long is remaining for the petition to be approved?

This is not an easy question to answer due to many variables like the USCIS work loads, number of petitions they are processing, the class of...

If my PERM gets denied and we file an appeal, if it is in progress I do H1 ext for an year, if it gets denied, my H1 is valid?

I agree with my colleagues. Your H1B should be still valid as long as you complied with the requirement (work for the company, etc).

I 589 is your petition. I 130's beneficiary is your wife. This will not affect your status.