1. Even though I have switched my employer, does it mean that my H1B stamped visa(with my previous employer) is still valid?

You should contact your new employer's immigration attorney to assist you.

You should contact an experienced immigration attorney to assist you.

How long does it take for a USCIS "Removal" to go into place from the date of an I-601 denial? What is the fee to appeal?

I agree with my colleagues. Your case has very specific facts that are best addressed by meeting with an attorney.

Can I re-enter in the United States

Generally speaking if you were deported then is a 10 year ban. You should bring your paperwork to an attorney to evaluate your options.

Can I have my family in the U.S. receive an I-131 re-entry permit while I am overseas?

You have the option to have the permit sent to you at the US Embassy. You nay have it sent to an address in the US.

Does the 601 waiver have a time limit for me to turn it in? Can I turn it in this year????

You should show all of your paperwork to an attorney to see if you are still eligible for the 601 waiver.

UK travel on H1-B

I agree with my colleague. You will need to contact a UK barrister to answer your question about work authorization in the UK.

You are the petition on the form I-751 as you are the one who wants the conditions removed.

Does she need to visit another time to visit me and then apply to k-1 visa or we're good because we saw each other?

You should definitely meet with an immigration attorney and show them all of your paperwork, Generally speaking, it would be good to meet again.

How can I obtain certified court dispositions for NJ and FL when all I have are the numbers that USCIS provided and I am in NY?

You will need to call the criminal courts in NJ and FL and request certificates of disposition for your crimes. You should meet with an immigration...