3 - How are we qualified to engage in discipline?
It's about accountability. I would hope & expect someone- a fellow Christian who is also a good friend- to point out if / when I am at fault. But I do think this only really works when you already have a strong relationship with that person. I don't think it would be right for a stranger or someone you had only just met to point out something to you as I don't think it could be done with the right level of sensitivity and grace.
I think you are right about how it works in practice. We, particularly in a culture where we are encouraged to be individuals - are very sceptical about people we don't know well coming to us and pointing out our faults. And so I know people who enter into "accountability agreements" where someone gives someone else the right to point out where they are going wrong.
But I think it may have meant something different in the setting in which Jesus was speaking and in the early church context which was much more geared around the community - and where the actions of one individual in the community reflected on how the community was perceived probably more so than today.
And in what Jesus says he seems to be saying that we have the responsibility to point out where a brother or sister is sinning. He doesn't dilute it by speaking about a brother or sister we are particularly close to.
Maybe the challenge behind this is to ensure that we have right relationships with everyone to the degree that we can go to them in sensitivity and grace.
Is this an unrealistic dream / is it something we should even try to aim for in the context in which we live or do we need to understand how to apply this teaching of Jesus in a slightly different way? Maybe by seeking to encourage that, at least, each person is in some form of "accountability" relationship.