Here are the last sentences. Thank you very much.
1) Ten students and two teachers (from each of the four schools) will take part in the mobilities of this two-year project.
2) The teachers and the students involved will be chosen by each school discretionally if the project gets te approval of the European Commission.
Does #1 mean that there will be a total of 40 students and 8 teachers among all the schools? If so, delete the parentheses. Everything else is fine.
2) The teachers and students involved will be chosen by each school separately if the project gets the approval of the European Commission.
(Or you could say "... will be chosen at the discretion of each school ..."