Can I travel abroad using my green card?

Travelling abroad in your situation is a risk.

Overstayed?

It's possible that you overstayed your visa. If you have multiple entry in your passport, you can try to enter the US but the CBP at the port of...

I want to know what I got to do by getting my fiancea his permanent resident green card

You facts are unclear. Please have a full and meaningful consultation with an immigration attorney.

My wife has an interview after canceling her asylum application. What is the worst thing that could happen ?

She will be denied asylum and put in removal proceedings soon. Then she will not be able to return to the States for a long time and will need...

Asylum

The U.S. will not inform the home country because the asylum seeker is seeking protect under the U.S. asylum laws. It will defeat the whole purpose.

Travel outside the U.S. immediately after Green Card interview (H-1B / H4 holders)

You can certainly disclose your travel plans but may travel on your valid visas and return to the US until your visas are valid regardless of the...

I-130/CP: Request to change the country of consulate for Green Card Interview

You can contact NVC when the case is ready for consular processing, HOWEVER, be mindful that you have to provide proof of residency at country B...

USCIS Has denied our I-130 claiming for sham previous marriage and not meeting the burden of proof.

I agree with my colleagues on this question. Consult with your attorney.

Am I a US citizen ( green card holder since 12 yrs old) if my mother is a US citizen?

Was your mother a US Citizen? There are procedures to get your naturalization certificate. You can contact an immigration attorney.

It's a bit more complicated than this. Your status between applying for TPS and approval is "period of authorized stay", however you overstayed...