1) yes, berufsbegleitendes Studium = attending university (possibly in the evening) while working in a job
2) FH = Fachhochschule. These are universities that are more practically oriented than "pure" universities. The "Diplom" is the (old) German degree, somewhere between a bachelors and a masters.
3) Hochschule = university. "High schools" don't exist in Germany. Universities usually have a "Präsident", schools usually have a "Rektor". In both cases it's the highest position.
4) Prof. Dr. oec. = Professor Doktor Oconomiae = degree for business and administration, in addition to a Ph.D. thesis one has to do a second thesis ("Habilitation") to get the title "Professor".
HSG = Hochschule St. Gallen
5) den Titel X zu führen: in Germany, titles are part of the name, and there are laws about when you can use a title together with your name. The action of doing this is called "den Titel X führen". So "die Erlaubnis, den Titel X zu führen" = permission to add the title X to your name
6) Diplomarbeit 2fach gewichtet = the diploma thesis counts as two items for the average = when calculating the final mark, the mark of the thesis is summed twice; as if there were two theses going into the average result with the same mark