Give the most accurate information. This question will appear few more times in her immigration journey. It's best to be honest and clear now than have issues later.
Nobody can guarantee or predict visitor visa application outcome.
The risk is always there.
Have you considered naturalizing in the US and then going back to the Europe?
No, you won't receive anything else from USCIS.
If there's anything to be remembered from immigration journey - case status means nothing 😃
Somebody must have pressed the buttons on your case 5 days late.
You will receive certificate of naturalization in the mail, often few days or week after passport arrives. So don't worry about that.
The problem is, there is no solid consistent evidence proving filing I-129F works. We know K-3 gets closed when I-130 gets approved, but we don't have anything to indicate K-3 forces decision on I-130.
The only thing USCIS will honor with great level of success is Writ of Mandamus. Everything else provides mostly psychological relief for petitioner (e.g. something is happening, case isn't fully stuck because I'm getting replies and various updates)
Totally agree with you on this one. OP should not delay N-400. They should apply as soon as eligible.
N-600 for child is a nice thing to have in the future, when parent or kid can afford it. In most cases yes, US passport is sufficient proof of child's citizenship.
Yes, they say a lot of things. Last time they said my naturalization case would take 7 months, but it took 3.5.
I wouldn't want to bloat this topic with examples (news reports and immigration forums) where US passport wasn't enough to establish US citizenship. I just know the problem exists.