Does celonis save the information of my processes internally? And am I allowed to use screenshots of the diagrams in my bachelor's thesis without fear of plagiarism?

Celonis Data Security is a bigger topic to just tackle here, however Celonis maintains the highest information security standards in order to protect your data. You can read more about Data Security here

https://docs.celonis.com/en/data-security.html#UUID-129a363e-a425-57b7-5d49-70006e55f234_id_DataSecurity-Whereisthedatastored