There are a lot of realizations for WGS84: WGS84 (G730), WGS84 (G873), WGS84 (G1150), WGS84 (G1674), WGS84 (G1762), and WGS84 (G2139); and the “Transit” in ArcGIS.
Thank you for your help!
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99% of the original question is solved here: https://support.esri.com/en-us/knowledge-base/wgs-1984-is-not-what-you-think-000036058
Meanwhile, for Nr. 2:
If you have a RTK GNSS the resulting coordinate system depends on your RTK provider. The settings of RTK caster is inherited by the rover practically (technically the output is always in WGS84, but the position is estimated relatively to the base station which could express the coordinates in different GCS and due to the relative manner of calculation the resulting coordinate inherits the base's GCS).
99% of the original question is solved here: https://support.esri.com/en-us/knowledge-base/wgs-1984-is-not-what-you-think-000036058