Fixing rusted out cylinder to raise the hatch in the back

HOW DO I FIX THE RUSTED OUT CYLINDER IN THE BACK TO RAISE UP THE
GLASS PORTION OF THE REAR ACCESS TO THE INSIDE OF THE CAR. THEY
ARE RUSTED OFF THE GLASS PORTION AND THE METAL PART OF THE
BACK…

I HAVE A 2002 JEEP LIBERTY THE LEFT TURN SIGNAL AND THE LEFT FLASHER , THE RIGHT ONE WORKS FINE,
DOESN’T WORK AFTER I PUT A NEW BATTERY IN IT AND THE BULBS ARE ALL GOOD, THE FUSES AREN’T THE PROBLEM AND THE FLASHER RELAY ISN’T THE PROBLEM, NOW WHAT…

First- Turn off your caps lock. Second, learn to compose more coherent sentences.
Replacement cylinders are available at auto parts stores if it is the cylinder that is rusted through. If the mounts have come off the car due to rust I don’t know how to procede, your post wasn’t clear.
Your left turn signal doesn’t work? Did you check front and rear? Are you sure the bulbs are all the right type?
You put a new battery in what, the car?
If your car is rusty enough to lose the rear tailgate strut it is rusty enough to lose ground on lights. Use a 12 volt test light to see if there is power to the socket, if there is and a good bulb won’t light, check the ground wire or connection.

Agree. If the mounts are rusted, a body shop will either be able to weld new mounts and patch the rust, or install a new/used window unit that is not rusted. Question is how it got rusted in the first place so you want to check for leaks and fix that first.

If the bulbs, flasher, and fuses are OK, then what’s left is the turn signal switch itself or bad wiring or rusted sockets for the bulbs. I’d check the sockets and immediate wiring with a meter first since that is the most likely.