Inscrivez-vous ou connectez-vous pour rejoindre votre communauté professionnelle.
of course not as grammar is only a tool and not everything.
I fully agree with Anayat, correcting instantly indicates that you are paying more attention to how the subject is being delivered rather than the content of the subject. In other words you are not interested in what is being said. A few quiet words of advice afterwards would be far more appropriate and no doubt more acceptable.
Not at all. Even in the classroom the teacher should not do so as it discourage the students. It can be done after the student completes his talk in a suitable way.