How to file a report of foreign national entering the country legally to give childbirth?

That does not sound like fraud. If you must, you can contact ICE and report the behavior. It will almost certainly not be followed up with so...

Last names in immigration forms?

Indicate the last name as reflected in your current and valid passport and lost "other names used" when indicated.

What is your sisters status and why can't she apply for her spouse? You cannot file for a petition for your brother-in-law but it has to be through...

Marriage based green card q: Receipt for i-130 Received, but three weeks later Receipts for i-485 and i-765 still not received

This is not something to be worried about as receipts are sometimes issued at different times even for the same application.

You should contact the NVC about this mistake so that your record is reflected appropriately.

How do I know if I filled up form I-864 correctly?

An attorney would need to review your previous I864 filing to confirm many things such as whether the correct version of the form was completed,...

You can wait a few weeks and then write to your local asylum office to inquire if you have still not received any notice.

Your second marriage is not recognized or legal under US immigration laws so you cannot petition for your second wife.

Shall I re-apply for SB-1 visa if it has been denied once or apply for Immediate Relative?

You should file a new I130 for your wife rather than the SB1 visa and the process will take anywhere from 9-12 months.

BIOMETRICS APPOINTMENT HAS NOT BEEN RECEIVED YET?

You could wait a few more weeks and if still no notice then you can write to the asylum office to inquire.