You have violated all terms of your LPR status without any reason(s). You may apply again to register US permanent residency.

In general, the last day of work not paycheck, if contract is silent on definition.

A valid marriage acceptable in Turkey, without more would be acceptable by USCIS.

If filed correctly the K1 is faster. To correctly file I129F for K1 visa, consult a qualified immigration attorney,

The passport obtained from filing N600 is for 10 years. The 5-year passport is without the N600. Going through the N600 is preferred saves money.

If a person is qualified and meet the eligibility criteria for benefits sought. You may not be required to leave US to begin application.

You have to reconcile your names on all passports with a certified birth certificate. So, they clearly reflect and confirm you are who you claim to...

For cases involving fraud and USCIS error in issuing green card, contact an immigration attorney ASAP for guidance.

A certified copy of birth certificate and a valid passport are sufficient documents. Passport is recommended to be valid for six months.

That's a very long trip you have to carefully plan with an immigration attorney. Prior to departure apply for reentry permit to avoid issues at...