My car was knocking and shaking when I got to high speeds so I took it to the dealership and they told me it was the struts and springs. I paid $500 to have it fixed and it was better for about 4 days but now it is back to doing the same thing it was doing before I paid to get it fixed. Now there is also a grinding sound with the knocking and the shaking is worse. When they checked it they said there was nothing wrong with the cv joints or the axle

This is an indication of a strut issue. The shocks dampen the spring in the strut assembly. IF you have loose fastening components or bushings or a bad shock in the strut you can get a violent shudder when you apply brakes on a down hill direction.

I can not imagine anyone using any vehicle with a wheel
noticeably leaning in or out

You actually, not only drive that way at low speeds, but at
higher speeds -enough said- makes no sense you would risk
your car & your life doing so

Obviously you paid a shop in a sincere effort to resolve some
issues

Here the thing

You can see & feel the wobble by hand,so both you
& any repair shop can see the problem !!

What sort of shop do you use, that gives you a vehicle
back in that condition & why are you here for us to guess
at something, when you should asking the place that took
your money, what's going on, or maybe check with a lawyer

My car was doing this and I had to get all new coil packs... Mine were replaced under recall at the dealership at no cost. If you take each code and google it, or even check a VW forum, I'm sure the members there can provide a lot more thorough information...... I have a 2001.5 Passat myself and when one thing goes out they all follow suit. I will help with some research for you and post back...... But I'd check the coil packs that sit atop the spark plugs.

There is no way ANYONE can tell you if your engine shaking problem is related to ANYTHING until the cause of the shaking has been PROPERLY DIAGNOSED.

With that said, it sounds to me like you may hve some valve lifters sticking or maybe some broken valve springs. I really do not see how any of the things you listed could be even remotely related to a problem like that. However, once again, we are GUESSING until proper diagnosis proves otherwise.

Check your struts and springs in the front end. It would appear you have lost at least one strut, and maybe a spring.

Get a second and third opinion from other local mechanics.
Does the shaking chang with speeds? It possible you have a tire with slipped internal belt.
Could be a few other things too..
Sound issue may or may not be related. Have more than one guy look at it.

1) Take car to non dealer shops willing to give FREE opinion

2) Not likely you have a shock in Driver Front wheel, more likely a strut. Not likely strut needs to be replaced, but strut has a STRUT MOUNT (3 bolts of which can be seen when opening your hood) below this it is connected to STRUT BEARING which below it connects to UPPER SEAT OF STRUT or SPRING INSULATOR, that if loose will rattle. Usually, shops will not tighten, because to tighten is same labor as replace the parts. (Since you already dropped $1000 on ToyotaDealer, ask them to tighten FOR FREE since rattle is still there.)

3) There is a part called a "link," connects strut to stablizer bar, that if bushings are bad will rattle.
4) If stabilizer bar bushing(s) bad, will rattle early on but eventually clunking
5) Bad ball joint or tie rod can rattle as well

Never permit any shop to do expensive work on your car w/o first getting a second opinion somewhere else first. Do not tell second shop that you are there for a second opinion.

Shaking steering wheel at highway speed, no braking
1) Bad tire in front, bad tires in front, verify inflation of tires
2) Wheel alignment may be out
3) Front suspension parts (mentioned several above)

Highway speed to suddenly braking shakes steering wheel
1) Front brake rotors need to be inspected for warping
2) Test calipers on empty road at 40 mph, going straight on very LEVEL ROAD, hit brake pedal SOMEWHAT hard while barely touching steering wheel. If car jerks to one side, instead of braking straight on, you may have a caliper, ABS, or brake fluid pressure regulator off.
3) If brake rotors are warped, may as well replace front brake pads at same moment. Use ceramic.
4) When you drive on VERY LEVEL road on highway, steering wheel must be centered, let go lightly of steering wheel. Did car stay in middle of lane? No? Get a 4-wheel alignment.

When you changed the struts,did you put in complete assemblies with new springs and top bearings?It is usually the top bearings that make noise when turning.Next is worn outer CV joints on the axles.

It is most likely the control arm bushings. These are notorious for going out on Cobalts. I have had mine replaced twice.

The control arms on both the driver and passenger side have rubber bushings which probably deteriorated. This is causing metal to hit metal when the car goes over bumps.

The bushings themselves are relatively inexpensive; you can most likely pick them up at a dealership for under $40. The only issue is installing them. You have to use a hydraulic press to press the old bushings out and press the new bushings in. This isn't difficult, but you need the equipment.

I agree. I see sway bar links go bad and make nosie much more often than struts on Ion's. Take it to a service center you trust.