What is the petition approval based on?

Your wife would have to sign off on an affidavit of support and/or have a joint sponsor sign an affidavit of support if your wife's income is not...

Could I apply to a EB3 VISA (the company which would hire me) if I've never had any work permission in the US?

You would need to consult with an attorney and explain your educational and work history , information about the employer and proposed employment...

Should we have to pay the USCIS? or can we ignore the letters with no further repercussions from any gov. agency?

It is not clear from your question what payment USCIS seeks.

After filing an I-485, does one have to remain in non-immigrant status in order to be able to receive a permanent resident card?

No, generally one must only have maintained nonimmigrant status at the time an application for adjustment of status was properly filed.

When and Where I can contact the pro bono immigration lawyers in NYC?

Contact the Immigration Court for a list of lower cost attorneys that may be able to assist you.

Having a green card, can I travel abroad as much and as long as I want or would it jeopardize the residency status?

You can jeopardize your residency status and future eligibility for naturalization.

Having a green card, if I change my working physical address, do I require to do any amendment (as it happens with the H1B)?

No, this would not be required since you are already a permanent resident.

What is a Sailing Permit?

This should not be needed for a short trip outside the United States. See https://www.irs.gov/Businesses/Departing-Aliens-and-the-Sailing-Permit

USCIS will not expedite an advance parole for a Honeymoon.

Will a denied I-485 hinder my chances at getting OPT a year later from now?

You should consult with an attorney if you are concerned with information you are obtaining from non-lawyers on the internet.