Regarding に, it's one of case particles. It describes movement and time. And in this case, it is about time 'When'. When I was at school,~' 学生時代に~
About '~はもちろんのことである’, in English, it is 'It goes without saying that~'.
In this sentence, a teacher feels quite happy not only when he/she has students who won some awards but also when he/she meet up with his/her former students and know their activities.