2000 Subaru Outback - shaking

My 2000 Outback is shaking - forwards to backwards - when I am driving, sometimes. The car is new to me, I’ve only had it two weeks. My dad bought the car and did a bunch of work on it. The timing belt and water pump have been replaced, also the spark plugs and wires. We changed the fuel pump and filter and adjusted the idle? (not exactly sure what that is, but my mechanic checked it and said it was idling normally). My dad is a mechanic, but he lives far away from me and he fixed everything he could think of before I brought the car home, so we are at a loss as to what else could be causing the car to shake this way.

The problem is unclear to me.
When you say that the car is “shaking-forwards to backwards when driving”, are you talking about a ride problem or are you talking about shaking that seems to emanate from the engine?

Is the problem not apparent when the car is stationary?
At what speed(s) is the shaking noted?
When you feel the shaking, is the engine’s power affected?
Is the Check Engine Light illuminated?
Is the tachometer registering a change in RPMs when you feel the shaking?
Is the problem only felt while braking, or only when not braking, or both?
Do you feel the shaking only while turning, or only while driving straight ahead, or both?

Do you feel the “shaking” in:

the seat (through your butt)
the steering wheel (through your hands)
the brake pedal (through your feet)
every part of the car

And, because of the AWD nature of the vehicle, here is a particularly relevant question:
Are all 4 tires of the same brand and size, and do they have equal amounts of tread wear?

???

I’m in agreement with VDCdriver as much more info needs to be provided because the complaint is murky to me also.

You refer to your dad being a mechanic. You do realize that the throttle plate screw is really not to be tampered with? Tampering with that usually means that someone is trying to override a problem they can’t figure out.

IF this is an engine performance problem the point could be made that the timing belt being off a tooth or two can cause a problem.