Added your info to spreadsheet.
1. Yes, fingerprints are for clearing criminality which is part of background check. Since your BG completed already, you will not be asked for fingerprints, unless in rare circumstances when the application is pending for over a year.
2. Per IRCC, you are advised to inform them via a webform if you are going out of Canada for more than 2 weeks. In case they schedule an in-person interview (which they do for certain cases) you are supposed to be physically present in Canada. If you are outside, you can inform them about the same and request for rescheduling it after your return and mostly they agree.
3. Minors kids are exempt from BG, Test, Language etc so you wont see any progress in their tracker for any of these. It will only update when they schedule the oath for the family.