Form I 130 submitted on line in Photomac center. Form I 485 and I 693 were sent to USCIS, FBAS, Chicago.Is it ok ?

No do not leave prior to receiving AP and be patient for remaining receipts.

Unclear why USCIS would update the name on your adjustment case. May be best to contact USCIS directly.

Yes you may through VAWA after 3 years.

Cohabitating with a known drug user of course comes with risks that you must be ok with.

Immigration question ? Crazy situation . Previously married and now remarried wanna file for green card ?

Yes based on the information provided you should be able to adjust status despite previous history. It is advisable to work with an attorney for...

Yes but you would need to petition with a probate court to do so.

Does the A material Witness get visa denied

No this is not a crime that should prevent your admissibility.

What documents can be used to explain/prove to USCIS that you never received their notice?

A statement from you to begin and from there it is best to consult with an attorney for guidance.

Can USCIS deny a petiton I-130 for mother who has 3 US citizen children and 1 immigrant child living in the US?

No this is not a basis for a denial of an I130 outside of other circumstances. Best to consult with an attorney for guidance.

Can I apply for change status of my Visa being in Puerto Rico?

Yes you may apply for a change of status in Puerto Rico.