Broken clutch fork? and transmission removal

I believe i have a broken clutch fork in my 2005 vw passat 4motion 1.8 t manual transmission

I lost nearly all clutch pedal resistance and completely lost use of my clutch the other day while i was driving. My slave and master cylinders seem to be ok and i cant see any fluid leaks anywhere in the system. Appearantly this issue could also be cause by air in the system but i don't know how that could have happened in an instant while i was driving like it did.

Anyway I removed the slave cylinder and was able to feel the top of the clutch fork and there was some movement in that fork. I was able to wiggle it freely a little bit. Is this a sure indication of a bad fork or is that normal?

Also can the transmission on this vehicle be removed without pulling the engine?

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