What is the ruling on the money that must be paid to the official after medical tests have been conducted without his knowledge and without paying their cost, and without knowing the specific amount?

The questioner is considered a private employee of the laboratory owner. A private employee is not permitted to act beyond the scope of what has been authorized for them. What the questioner did, performing free analyses for her colleagues, was not authorized and is considered a breach of trust and an infringement upon the rights of others.

She must repent and advise her colleagues. Part of complete repentance is seeking forgiveness from the rightful owner and requesting his pardon. Otherwise, the right must be returned to him by estimating the amount due for the analyses performed and returning it to its owner by any means, even without his knowledge of what truly happened. There is no harm in her and her colleagues collaborating to collect this amount.