Actually, the WRX wagon suspension is about the softest there is on an Impreza for 05. And yes, the tires really are that crummy. Good news is, it's not as bad as you think- after driving what is arguably the best handling factory-built car on the road, I'm not surprised you hate the wagon.
If you want to improve your car's handling, some simple steps will help tremendously. First, get some 17" wheels with performance tires, to add grip and sharpen response. Second, get a sway bar package, particularly the rear. Then, decide how stiff is too stiff and pick either a set of springs, or some coilovers.