You would want to file a K-1 visa, but must marry within 90 days.

As a E2 visa holder, do I need to pay taxes in the US on my worldwide income?

Very interesting question, but as pointed out better suited for a tax lawyer.

My wife (petitioner) submitted the I-130 back in March 2015. Now we have received a I-1797 with approval.

Your timetable is correct. Add a little patience.

Can a Mexican Immigrant w/ no US documentation take a closed loop cruise from Florida to Bahamas using a Mexican passport only?

The issue seems to be whether he will have to clear CBP on his return. Check with the cruise line if that is likely.

Do I have to change my name on my green card and passport before I travel overseas if I did a legal name change?

Best to wait and travel based on current name. No sense making waves now.

Does nvc and the consulate both has to review ds-260 form beforeNVC close the case and FWD to the consulate to SDUL visa intview

Consulate uses it connection with your interview only. NVC actually reviews it.

Applying Green card for parents ,But don't have Birth certificate. please guide.

Provide secondary evidence such as a baptismal certificate.

Was this really deportation?

Your question is confusing. You say you did not cross the border but returned to Mexico....three times. It is possible that your "returns" were...

This should not affect the process at all.

How can I replace green card in less than 4 weeks?

File I-90, get Infopass appointment, have passport I-551 stamped, enjoy trip