Sorry, but you are starting over.
With immigration you really need to pause, count up to a 1000 and then proceed with action. Especially if it's a cancellation.
Mmmm... Not 100% true. Officers have discretion to ask about travel to other countries as a way to prove that the applicant is not just trying to establish themselves in another country.
What country are we talking about? That's important information that will give you a more accurate reply.
Is there an age difference?
Has the petitioner applied for a visa before?
This person has already filed their 751. And no, it does not always "stick". When I filed for N400, a year after my 751, USCIS sent me to my older State for biometrics.
My 751 was approved about a month before my N400 interview. I do not remember the wording of the interview letter, but I did attend with my husband and I am glad I did because the officer did ask to see him. Officer made it clear he was unaware of the approved 751, so maybe your situation is similar. I would not worry (but I would go with my spouse)
No, no need to bring them and often seen as a nuisance in the context of a formal interview. However, do bring documentation that proves that the children were born to this marriage, such as birth certificates, school records, and family pictures.