I am a US Citizen. i filed for my stepdaughter in 2016 and was approved 2/2018. has not been sent to nvc. is this delay normal?

I am just curious, how is it that you did not reach out to USCIS or the NVC? Did your Congressperson mention whose background is being checked and...

Immigration - green card and naturalization?

This split up/divorce, by itself, will not cause you to lose your green card or otherwise affect your filing for citizenship in the future.

Can my wife return to the United States from Mexico while awaiting the results of her permanent resident visa medical exam?

You need to consult with an experienced immigration attorney.

How can my boyfriend soon to be husband/father of my soon be be daughter see if he has a clean background?

I agree with my colleague. The lawyer may also pull his FBI, ICE, CIS, etc. records that may exist.

How to obtain a sworn statement for the replacement of Certificate of Naturalization?

Your statement written by you or by someone else on your behalf must be notarized.

Applying for asylum status being relative to a special immigrant (i-360 approved)

He can apply for refugee status. Or, you can file for him when you become a U.S. citizen.

Change name from ex name to current husband name

You should really consult with an immigration professional. You plan to file to lift the condition from the green card that you got through your...

Can we submit same evidence in I-751 that was submitted in I-130? I-130 was submitted outside of USA at an Embassy.

Yes, plus the additional two years of evidence, prior to the filing of the I-751.

No trouble because of the marriage and divorce; unless fraud was involved. You qualify to get for your citizenship in 5 years.

Are biometrics from I-130 reused in I-751 if it's only been 2 years since biometrics were captured at the time of petition?

They could if they wanted to. But CIS usually do an update, not necessarily a full set of prints.