Does money earned from a study leave constitute a dubious earning, knowing that I am not actually training at the foreign university and cannot inform the college to stop the salary?

To be eligible for the scholarship, the condition of being on an academic mission must be met. If the questioner was not actually on an academic mission at a European university—as she claims—then she has no right to receive a scholarship salary. Her work in medical statistics for academic theses is unrelated to her university's tasks, otherwise, she must provide proof of that to the university.