How to calculate an angle?

does 3D Slicer have any international approval for medical use?

Slicer has been used clinically in many projects in many countries, as described in thousands of papers that cite Slicer (see a selection here). For each use case, it is your responsibility to ensure that Slicer fits for the purpose and obtain the necessary approvals. See more information in these related discussions:

Yes, and there are several options. Your question has been already forked out to this topic, let’s continue the discussion there: How to define vessel centerline