levirroh

You have an ongoing investigation for fraud and you think that USCIS should have focused primarily on your marriage? Even though there are ways for Americans to bring loved ones to the country, the USCIS is more concerned about what's good for the nation than for keeping that citizen happy. So if they are concerned that you are going to be a bad resident due to an ongoing investigation than that will be their focus. In addition if they believe you're involved in one fraud, it would be a natural assumption that you wouldn't feel bad committing immigration fraud as well. Have you consulted a criminal attorney about the criminal investigation? If you have, be sure to tell them what you said. I would assume that your statements would be admissible in court. And the next time you get called to USCIS for an interview, take a lawyer.

You should be able to get back in with no problems... But cbp officers are known for their erratic behavior, so I wouldn't say 100% chances

I am in the same situation. I also got in on a B-2 visa and got married some months afterwards. We sent in the AOS yesterday
And I would love to travel to my country sometime this summer to take care of business, my stuff and see my family.
From all I have read, once you have the Advanced Parole you should be able to travel.
Like everyone else said: you came in legally and you did not overstay as the moment you apply for AOS you should not even leave.
There are two little concerns here:
We asked advice from a lawyer before we did everything ourselves. He said the AP is not meant for extensive travel and he had a couple having problems because they stayed away too long (a month). In the meantime they missed the interview... so then you can start all over again.
I wonder about the experiences of other people here. How long they stayed away on the AP.
Also: it says with all the Advanced Parole instructions that it's not a guarantee you will be let into the country again.
But they say that with the VIsa's and Esta's as well so I think in a normal case they would let you back in as your petition is still being processed.
Good luck and hopefully you get your AP soon!

PD is priority date.
Do you have AP? If yes, then yes you can travel. If not, then no.

a 3 year ban is for if you stay overstay for 180 days. A 10 year ban is if you overstay for 365 days.
So if you've already filed your AOS, then you are legally allowed to be in the USA and are not overstaying right now.

I am assuming your b2 is expired correct?

PD = petition date?

1. You have never accrued any unlawful presence. You do not accrue unlawful presence while AOS is pending
2. Even if you have accrued years of unlawful presence, that does not affect your ability to travel on AP and come back

Most likely you won't have any problems