Please Help!

Sounds like bad gas after storage - did you get all of the old gas out of there? I'd put a fuel pressure gauge on the car and see what it's doing. The sock in the tank may have gummed up, my dad's car did that and we had low fuel pressure despite new gas, new filter, and a good pump. That would require pulling the tank / pump unfortunately. Pull the engine codes to see if it's something else -- replacing electronic parts on a guess isn't a good use of time or money.

The stick shaking might be some binding u-joints or just some flat-spots on the tires after storage. It could also be the car just running crappy from the other problem. If it's the tires they should eventually get their shape back - next time try over-inflating them while it's stored. If it's the U-joints definitely check them for binding from dry grease. It could also be a lot of other things but those would be my first guesses.