Car shakes when clutch pedal is pressed all the way to the floor

The short answer is yes it is most likely needing a clutch repair. What is most likely happening is when you push the clutch to the floor, the actual disc is not fully disengaging from the flywheel so the vibration you are feeling is the engine pulses due to it not being separated.

https://www.2carpros.com/articles/clutch-symptoms

So the clutch disc may not be in need of replacement but it is more of the hydraulic side like the slave cylinder is not moving the pressure plate enough. However, if you are going in to do one part, you want to replace it all while you are there. This is not a job where you only do the one part that failed.

https://www.2carpros.com/articles/clutch-doesnt-work-sometimes-or-not-at-all

I attached a few guides that will help explain this in more detail. Let me know what questions you have and we can go from there. Thanks

They call it the clutch actuator cylinder but it's the slave cylinder. It is located inside the bell housing.

Yes, this could be caused by the actual bearing but you are feeling it because the other components are worn as well. When you are pressing the clutch you are putting pressure on the bearing so it doesn't vibrate but when you get the end of the pedal travel you can start to feel it again.

Sounds like a typical clutch that is at the beginning stages of failing. You don't need to do it today. More then likely you will start to notice the shifter is harder to get into first gear and then you will hear some grinding when shifting into different gears even though the clutch is all the depressed.