The car appears to be floating away or gliding out of control after driving at a speed of above 80km/h, almost as though I am driving on a slippery surface
Is this the shocks or stabiliser rubbers? What else could it be?
Motor Vehicle Maintenance & Repair Stack Exchange is a question and answer site for mechanics and DIY enthusiast owners of cars, trucks, and motorcycles. It only takes a minute to sign up.Sign up to join this community
As Solar Mike said, other mechanical problems can cause what you're experiencing.
To answer your question: yes, the two faults you ask about could cause or contribute. The stabilizer mounts (rubbers) by changing the response of the stabilizer bar(s) from moment to moment, or when forces on the mount(s) change direction. The shocks, if worn, will do a poor job of keeping the tires in contact with the road surface, thus affecting traction. Correctly-performing shocks — that is, not worn out — will, in turn, do a better job.
To ascertain what's going on, all of the car's suspension components will beed to be carefully examined to determine which of them are worn or faulty. There are a lot of them: tires (enough tread? correctly inflated? not bulgy in the sidewall or otherwise failing? not so old that their traction is impaired?); steering components (rack or steering box, tie rods, steering links, and the joints that connect these parts); suspension bits (shocks, including their state of wear, springs, and all these bits' mountings, suspension arms and their mountings and joints and pivots).
On top of the already goven advice: I'd check your (front) toe-in/out. Toe means the inclination of the wheels to either the out or inside of the vehicle by some degree. Your wheels are usually not exactly perpendicular to your vehicle when the steering wheel is in the middle, but off by some degree for compensation for play in the suspension.
Rearwheel driven vehicles usually have 0 degrees toe or a little toe-in on the frontwheels to compensate for force by drag and braking. Frontwheel driven vehicles usually have a little toe-out on the frontwheels. This is to compensate for the force on the front wheels put there by the engine to drive the vehicle. An excessive toe-in makes for nervous steering behaviour, excessive toe-out makes for an experience like you describe.
For a serious diagnose you should go to a workshop, but you can see it for yourself if the toe is off by a great amount.