pushbrk

Correct, but maybe not all in just that language.  Just going to take a minute to encourage any reader to assure the US Citizen or another native English speaker with good language skills be taking the lead in managing their visa process or the process for their foreign spouse.  When language skills are insufficient, instructions get misunderstood.  I posted the relevant section of the instructions, but if a person doesn't understand the meaning of "waived" within the context of the sentence, then their language skills are insufficient to effectively follow many other instructions as well.  
 
Further, when the US Citizen spouse is not involved enough to take the lead on these matters, it indicates some other potential red flags are present.

What country are we talking about? 

Can you please fill out your timeline and profile so that our answers can be more specific to your country?
 
I for example was able to get a international version of my/children's birth certificate and marriage certificate with one line being in english.

I scanned in documents with a software (got it online for free) which lets you scan documents and then transforms them into a Word (with pretty much the same formatting). That way you only need to translate and the document looks pretty much the same as the original.

Three people and the Department of State website say you don't.
 
You can go to Dubai and get one if you want.

Your service center has nothing to do with Visas. You will be sending your Petition to one of the two lockbox. According to assignments they will send to a service center. You will know when you receive your letter from USCIS.
Visa's are handled by the Department of state NVC/Embassy a whole nother matter.

I would save the money and send him by yourself.  There's no need for you and the kids to attend the interview.

And what we are trying to tell you is there is no way to know for sure. The State Department does not provide that statistics and their official warning is: "Do not book flights, sell your home, quit your job or making any irreversible life-altering decisions until you physically have the visa in your hand"

Your income, affidavits, and employment verification can be left out.  You've got plenty.  Deal with your current income and past income at the NVC stage when you submit the I-864.  Your family connections and six visits over a three year relationship will carry the day.  Try to limit your evidence to less than 30 pages.

Your income, affidavits, and employment verification can be left out.  You've got plenty.  Deal with your current income and past income at the NVC stage when you submit the I-864.  Your family connections and six visits over a three year relationship will carry the day.  Try to limit your evidence to less than 30 pages.

4. above is incorrect.  He can use the combination of the visa and stamp next to it to enter the US for a year.  Once used, the visa expiration is irrelevant. 
2.  Since the spouse has an immigrant visa, he is NOT coming on a visitor visa.
1.  Visas are valid for 6 months from the completion of the medical, not from the issue dates.

Get a new passport. No issues whatsoever. 

Correct.  Do not get current country police report until after petition approval.  In the meantime, study and prepare.

I had time look at you other posts. . .  Are you sure your step daughters father can't transmit citizenship to her?  If he has lived 5 years in the US, 2 of which after age 14, prior to her birth she can file a late CRBA and you are done.  He doesn't have to co-operate.  If the CO determines that he "Could have" transmitted citizenship then your step daughter will be ineligible for a US VISA.
 
We didn't have kids involved in our case and I didn't even marry a Mexican.  I have permanent residency there so we processed thru DCF quickly.   But I volunteer for a NGO doing immigration so . . . 
 
If you can't get the citizenship:
 Do a signed notarized letter from the US from the father and preferably a copy of the bio page of his US Passport.   Or one from the Mexican side.  English is preferred.  Otherwise someone can translate it.  Mexican Notorio isn't the same as Notarized.  Witnessed by another party is fine. Include his CURP number and copy of the IFE or Mexican Passport Bio will suffice.
 
The letter should say that the daughter is allowed to immigrate.  
 
If you are filing stateside . . .
Documents that are included with the petition or go to the NVC should be translated.  Spanish documents are ok at the interview.
 
If you have Mexican Residency you can still file DCF in Mexico City and save some time.   Unfortunately stateside spousal petition interviews are very backed up in CDJ.   DCF interviews are faster.   Ours was 2 months after documentary qualified while stateside petitions were taking 7 to 9 months.  Stateside is taking even longer now.
 
We haven't been to Mexicali since last spring.   My favorite Chinese restaurant, in the world, is Jing Wah.  And I travel to China often.

Since the other case will never complete, the above is accurate.  
 
To the OP, the lawyer was wrong.  

Of the visa applicant.

Often people use the wrong words, or misinterpret the correct words.  If the visa is in his passport, it will be used upon entry and a stamp next to it substitutes for his green card.  Just take the green card to him when you go to sort things out in Switzerland.
 
 

Often people use the wrong words, or misinterpret the correct words.  If the visa is in his passport, it will be used upon entry and a stamp next to it substitutes for his green card.  Just take the green card to him when you go to sort things out in Switzerland.
 
 

Often people use the wrong words, or misinterpret the correct words.  If the visa is in his passport, it will be used upon entry and a stamp next to it substitutes for his green card.  Just take the green card to him when you go to sort things out in Switzerland.
 
 

Nope you will be totally fine! His visa will be activated once he enters for his business trip and from then on is a permanent resident

Perhaps you cannot add a joint sponsor because you qualify on your own.  No, the petitioner does not submit evidence of US Citizenship at the NVC stage.  You did that with the I-130 already.

She is the US Citizen.  She can move to the US anytime she wants.  He is the one that needs the visa.

She is the US Citizen.  She can move to the US anytime she wants.  He is the one that needs the visa.

I'd ask over here https://www.visajourney.com/forums/forum/93-canada/

Having a child does not make it that much more complicated.  She should investigate if she qualifies to pass along US citizenship to the child which could make that part easy.  Then I would suggest legalizing the marriage and then filing for a spousal visa. 
 
Good Luck!

Personally, I would unless you really need to travel immediately.  The ROC process is not super hard, but it is a pain, and with five weeks, I would wait and skip that step.
 
Good Luck!

Correct, because she cannot use his income.  Counted in household size is not the same as "qualified household member".