pushbrk

As noted above, if the child qualifies to derive citizenship from you (generally 5 years of physical presence in the US, 2 of which past age 14), then the CRBA process is what you need. They will get a US passport.
 
If you don't meet the requirements to pass citizenship, then:
1) The child needs their own passport and visa to visit the US.
2) No, you cannot come to the US with intent to stay/file for permanent residency. It would be fraudulent to use almost any non-immigrant visa to do so (certain work visas and special cases are exempt).
3) You would need to file an I-130 for the child. You cannot add them as a beneficiary to the existing I-130 since there are no derivatives allowed in the CR-1 or IR-1 category.

All good.  Did you have a traditional engagement ceremony.  Your age difference is not uncommon for Vietnam, but she may well be asked extra relationship questions and questions about your life, family, ex wive(s) and work.  Provide plenty of relationship evidence when filing the petition with focus on evidence of time spent together in person and the engagement party.
 
 

All good.  Did you have a traditional engagement ceremony.  Your age difference is not uncommon for Vietnam, but she may well be asked extra relationship questions and questions about your life, family, ex wive(s) and work.  Provide plenty of relationship evidence when filing the petition with focus on evidence of time spent together in person and the engagement party.
 
 

If a person is asking a tax question related to what is "proper" as a filing status, the above is correct.  In the context of immigration process and procedures, since late 2005 when I started watching, I have never seen any consequence to filing single and paying extra taxes.  The petitioner is well advised to amend the return when the beneficiary has a Social Security number, and get a refund for their previous overpayment.
 
During my entire life, I've never seen or heard of the IRS penalizing a person in any way for paying too much federal income tax.
 
A Caveat is that if you are an employee of the IRS and file with the wrong filing category/status, expect to lose your job, but those people know that already. 😉

With the exwife on a tourist visa, you would have filed a i-130 for her concurrently along with the i-485...which is a petition.
The answer is YES.

If a person is asking a tax question related to what is "proper" as a filing status, the above is correct.  In the context of immigration process and procedures, since late 2005 when I started watching, I have never seen any consequence to filing single and paying extra taxes.  The petitioner is well advised to amend the return when the beneficiary has a Social Security number, and get a refund for their previous overpayment.
 
During my entire life, I've never seen or heard of the IRS penalizing a person in any way for paying too much federal income tax.
 
A Caveat is that if you are an employee of the IRS and file with the wrong filing category/status, expect to lose your job, but those people know that already. 😉

You missed reading the further instructions on page three.

if you lived in the country less than 12 month no need for police certificate 

You don’t need to register it again. The US recognizes all legal marriages overseas. 

Risky to try to enter again until he has been gone as long as his last visit lasted.  To do so can be construed as an abuse of ESTA, or the VWP.  But, as stated above by LilyJ, it is not specifically forbidden to enter sooner.  It's always a judgment call.

Passport is proof 

Records for the USA are not required. They will already have access to her record over here. 
 
As an aside, since you have waited so long for the NOA2, any police certificates from other countries where she previously lived could have been obtained prior to receiving the NOA2 as they have no expiration date. Time spent waiting can always be put to good use in this process. 
*~*~*procedural question moved from “progress reports” to “process and procedures”*~*~*

I would try it.  It's just another form and package of papers.  It won't hurt.

Information from three tax years is required.  If things will be pretty much the same, in terms of job and income, just including the latest return is probably fine.  Sending the other two transcripts won't hurt anything.  You need them to get the information from them anyway.

If they contact you again, just indicate you are withdrawing the petition and filing an I-130.

I recommend wet signature on the I-134.  Everything else IS a copy anyway.

Information from three tax years is required.  If things will be pretty much the same, in terms of job and income, just including the latest return is probably fine.  Sending the other two transcripts won't hurt anything.  You need them to get the information from them anyway.

I would try it.  It's just another form and package of papers.  It won't hurt.

Current income is the primary factor .. but IO makes their decision on circumstances as a whole.  You can  line up a joint sponsor do you don’t delay if needed .. or you can wait until the decision at the interview .. 
 

You would need to contact the county office you got married in to see about getting it corrected. What ever agency that issued the license will need to advise how to correct this.

https://travel.state.gov/content/travel/en/us-visas/visa-information-resources/ask-nvc.html
 
 

No DCF for Brazil except in very limited cases. Stateside filing will be the path.
 
Edit: Note that it’s the USCIS I-130 path in both cases. One is stateside filing and the other is via DCF.

You are not required to use a lawyer for either the process you are in or an IR1 visa.  If you have a lawyer now, hopefully he is pressing USCIS for an expedited approval of your wife's advance parole.  You can also seek assistance from a local politician.  I recommend contacting your State's Senior US Senator's office most local to you.  The best solution is to get that advance parole so she can attend the interview.
 
If you decide to withdraw the AOS, you'll still need an approved I-130.  Worst case is you go to the interview alone and get done whatever you can at that time.
 
If you hire professional assistance, hire a professional proficient in Family Based US immigration.  Start here.  https://www.visajourney.com/partners/

I'm assuming he entered the US illegally and now needs to interview abroad (hence the need for an I-601A). The unauthorized work isn't an issue for a CR-1/IR-1 visa.

FYI, the Texas Service Center, in Mesquite, TX is about 30 miles from the Dallas Lockbox (intake) facility that is actually in Lewisville, TX.  Where you mail and where your case ends up has not been connected for several years.