Regarding the feeling of the motor almost falling off when shifting, this is *not* normal. This sounds like a serious problem, potentially related to:
* Transmission issues: Worn-out transmission components, low transmission fluid, or internal transmission damage could cause harsh shifts and the sensation you describe. This is a significant concern.
* Engine mounts: Worn engine mounts can allow excessive engine movement, leading to vibrations felt during shifting.
* Driveshaft or axle problems: Problems in these components could also cause vibrations and harsh shifts.
Do not continue driving the car in this condition. This sounds like a potentially dangerous and costly repair. You should have a qualified mechanic inspect your Taurus immediately to diagnose and repair the problem before further damage occurs. Ignoring this could lead to more extensive and expensive repairs, or even a breakdown on the road.