Is one obliged to follow a PhD / doctoral school program?

The thesis Director may require the PhD student to follow such a training.

How does one remain registered for the thesis if the master is completed?

A certification by the thesis Director confirming that the student is hosted in his laboratory is required; the procedure is then automatic.

When one is writing a PhD thesis, does one have the right to re-use texts or parts of texts from other masters or other documents?

No! This is plagiarism and, as such, considered as a very serious matter. The penalties can be very severe. For more details, see the page on the policy on plagiarism at the University.