Is it permissible to grant certificates for training courses with information that does not conform to reality (start and end dates of the course, number of attendance hours) after students have passed an exam or pledged to complete the course later, while collecting fees from them?

It is not permissible to issue certificates with incorrect data, dates, or attendance hours, because that involves forbidden lying and deception. A severe warning has been issued concerning both; for truthfulness leads to righteousness and Paradise, while lying leads to immorality and Hellfire, and whoever deceives is not of us.