Piotr

1) I'd check the flex disk. It is not difficult to replace if that is the problem. Then I'd go back to the tires. You say they are balanced properly. I've had tires when cold they would be fine, when hot they were out-of-round due to ply separation. Also check that the wheel bearings are tight. Jack the car up, grab each tire top and bottom and see if there is any play.

2) I'd check the front ball joints, though that doesn't jive with the rear squeak.

3) well let me go on to 4

4) Bad rear shocks can make the car feel like it wants to swap ends in hard turns on rough surfaces. Two inches is a hugh amount, and the mechanic said the rear shocks are okay. Was the car level before you did the front shocks? If it was the shocks may be improperly installed or the wrong shocks. Do you have the self leveling rear suspension or aftermarket springs with perch kits? The car is skittish. Are all the tires the same brand and size? This car should hold the road like glue.

5) Goto #1.