"Can MetaTexis run while other CAT tools like TRADOS and Wordfast are running at the same time? Are they compatible?"

Yes, in principle, MetaTexis can run in parallel with other CAT tools.

However, if you use shortcuts, you are advised to de-activate either MetaTexis or TRADOS/Wordfast temporarily because some of the shortcuts are identical (if both MetaTexis and TRADOS/Wordfast are active at the same time the behavior of Word can be confusing).

When you use MetaTexis, TRADOS/Wordfast should be de-activated. You can do this via the "General options" dialog of MetaTexis. However, you will automatically be warned of this when you load a MetaTexis document.

When you use TRADOS or Wordfast, MetaTexis should remain temporarily inactive. You can do this via the MetaTexis sub-menu "Tools". Click "De-activate MetaTexis" and chose to de-activate MetaTexis temporarily.

(If you are only using menu commands or shortcut buttons, or if you customize the MetaTexis shortcuts in a way that there are no intersections with the other cat tools, you do not need to de-activate any cat tool.)