forester2002s

One other, often overlooked, maintenance item: Change oil in rear-differential. First, check for oil leaking from the differential, especially from around the input-shaft, and from around the left and right output shafts. Ideally, the differential case should appear dry and not oily. If there is evidence of oil leakage, then the oil-level should be checked, and it's not much extra work to drain and replace the oil. However, if the diff-case is dry, with no apparent oil-leakage, you might be tempted to leave well-alone; but it's really not difficult to drain and change the oil. There should be 2 plugs on the the rear face of the diff. Use a 1/2"-square male driver to release the plugs. Always remove the top (filler) plug first, in case the plug is seized. On most Subarus, the rear diff takes about 1L of 75W-90 gear oil. The trick to filling the fresh oil, is to buy a cheap 'turkey baster' (squeezy-bulb type), and use that to get the fresh oil in through the upper fill-plug; fill until the oil reaches the bottom of the fill-plug. And you're done.

While you're at it, it would be a good idea to replace the fuel-filter (the black canister that one of the fuel-lines is connected to).

https://www.ultimatesubaru.org/forum/topic/145506-ej251-engine-weighs-119-kg-262-lbs/?do=findComment&comment=1222275

Agree on both points. Electric gremlins are difficult to corner and deal with. And there are multiple ground-points to worry about. My philosophy on grounds is that you can never have too many grounds (I'm not totally convinced that this is always true). So rather than chasing bad grounds, it might be quicker to just add grounds (in strategic places).

Is anything interfering with the clutch pedal? Carpet or mat for example?

I've replaced the brake-pads (front & rear) on my 2017 Forester. And with no problems. But my Forester has the old-style hand-brake lever - no electronic brake gizmos.

Oil change/flush might help?

I would be tempted to to try a thicker grade of oil (but still within the recommended range).

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.

Could it be a problem with the wiring between the speed sensor and the cluster?

A reminder: Take photographs of the old timing belt before removal, including timing marks. It will make installing the new belt easier.