forester2002s

My first thought is the rear drive-shaft (prop-shaft) bearings. But these usually cause vibrations when transmitting torque, for instance when accelerating in AWD. Same goes for the wheel bearings and half-shaft bearings. So it is unlikely that you'd feel any vibrations in FWD, with no torque to the rear end. So that leaves the rear-diff. I wonder if the rubber mounting-bushings on the rear-diff are failing. With no torque on the rear-end (when in FWD), perhaps the rear-diff can move around a bit, and this may be felt as a 'vibration'. I dunno, this is just my best guess.

Flakey ignition-switch?

Sounds to me like the rear drive-shaft, even though you've said that you have checked it. They are difficult to check by hand, but can you get a crowbar on it to see if it's loose?

Low compression reading? And same reading on all four cylinders? I would suspect a problem with the compression gage itself.

Could be lack of fuel? Either low tank level, or something else related to fuel?

You shouldn't need a heavy-gauge wire to energize the solenoid. 16ga would work. And we're only talking about a few seconds anyway.

For a quick test of the starter: - disconnect the small-gage wire that connects to the starter solenoid-terminal; - connect a wire to the positive battery terminal; and touch the other end of the wire briefly to the starter-solenoid terminal. This will put 12V to the solenoid, and should energize the starter itself. But be aware that the test-wire from the battery will be unfused, and capable of conducting a larger than intended current.

On most models, all the warning lamps are tested during start-up: - turn the key to the ON position (just prior to turning the key to START the engine); the display should show all warning lamps illuminated, including the check-engine-lamp; this verifies which warning lamps actually work (or not).

Seized rear-diff?

Recently filled-up with (bad) gas?

10%? That seems way too large a difference.

Could be a CV-joint, especially if the vibration seems to be from one wheel only. And more likely a front CV-joint, as you say that the steering wheel shakes. Or could be the universal-joint and/or support-bearing on the rear drive-shaft.

If it has a cracked head, the coolant likely leaks, and it may have a history of overheating. Beware!

Does the car still have the original engine?

Aside from the same-diameter situation, I would expect that (or at least not-be-surprised if) on-highway driving performance would be affected. I'm thinking that different manufacturers would have their own preferred tread-design and configuration of internal metal/fabric plies. Just how any of this might affect emergency swerving or braking, or cold-weather grip, is an open question. Personally, I wouldn't risk it.