Someone sent in a fake letter to UCIS stating they were me and that I committed marriage fraud Immigration

You already wrote to USCIS without know for sure that the ex-girlfriend's letter was received, taken seriously and added to your file? You should...

Green card for my adoptive daughter

You need an immigration attorney. Specifically you need an immigration attorney that handles adoption issues because they can get complex.

Husband got arrested yesterday afternoon (shoplift) less than $50 dollars, he is in process of getting his residence.

At the interview, be sure to admit the incident. They probably won't approve the case until the criminal matter is resolved. I would expect the...

Pending uscis case,seperated,met someone else and want to remarry.How will this affect me?

Of course this will be a problem. In the eyes of USCIS, this will reek of red flags. You REALLY need an immigration attorney whether you stay with...

Will a pending judgement affect my H1B Extension/Green Card filing?

No. Irrelevant to adjustment process.

I am a green card holder since 1992.

Are you currently in the US? Have you lived here since August 2012? If so, I think you're fine. You should consult with an immigration attorney to...

My UK Visa waiver ends 6th Nov 2013. May I leave for Philippines tomorrow Oct 25th, and return into US on Oct 30 for one week?

As long as you don't overstay, you SHOULD be okay to re-enter on VWP. However, if you've overused (vague, I know, but CBP has broad discretion...

Immigration case ,adjustment of status

Get an attorney so you can move forward. There are some good immigration attorneys in Iowa. Hint, hint. See above.

FBI report should suffice.

Entering US with employer other than petitioner when I-485 is pending

You really need to consult with an experienced immigration attorney on this. Not a simple case and more info is needed.