When do I need to leave my home country after being accepted for a Green Card?

You must enter the US within 6 months of issuance of visa.

Immigration: I have applied for green card based on my spouse's employment-based, when can I withdraw?

What application are you looking to withdraw?

Should I file I-864 or I-864EZ for my spouse?

You would use I864 and may need a co-signer. You will also need to re-establish domicile. Consult with an attorney for guidance.

Can I lose my green card status by living outside the USA on an extended basis?

Yes this prolonged period likely resulted in the abandonment of your residency. Consult with an attorney for further guidance.

We got married before the 90 days of the K1 visa. Can we still wait a little more before doing the Adjustment of Status?

Yes you may wait to file the AOS but advisable to do so as soon as you are able.

Yes you may do so and it should not impact your case given the nature of your filing.

What does it mean when US embassy says 'please submit you renewed passport to move ahead with you visa case?

Generally that the Embassy can issue your visa however more information is needed at this time. Consult with an attorney for guidance.

Can I obtain a letter verifying my citizenship from a local immigration office?

No you must apply for a replacement certificate or obtain your immigration record by filing a FOIA request.

Will uscis know if I sponsored or signed a form I-864 before?

Yes you will disclose that you have previously sponsored on the I864.

Will visa officer hold it against me if we sue them for taking 6 years to solve a visa case?

It is best to work with an attorney prior to acting, particularly suing.