Not necessary - but very helpful. It's not binary, but if you run a regression of course there's positive correlation.
Is it necessary to have an outsdanding school and university record to be able to work in the biggest consulting firms?
it is not necessary but helps a lot. If you are not coming from a target school or your grades are not great, you can still have options to be invited but you will probably need an internal referral. You can find more about referrals at the following link:
It depends on what else you have in your resume. It's not a must if you have a good career track
Depends on the office (country) not company. Some offices have strict target school policy, thus they do not review applications from other schools. However some offices would accept applications outside their target schools, there are many examples of this.
The higher your academic performance is, the easier it is to get noticed (especially if you have no work experience and come straight out of college for an associate/analyst position).
If you have multiple degrees (ex. BA and MBA), the last one matters the most.
If you have achieved great things during your professional career, maybe your academic track record will be put into second place.
No, absolutely not. I know people who were invited to MBB interviews without having received a degree from a target school. Once you're invited, your school doesn't matter. Just give it a shot:)