Misfires, shaking, rattles and power steering, rough idle.
 

I have an 04, with 45,600 miles. Just bought it.
First problem. Misfire on 2nd cylinder. I changed all 4 plugs, then coils 3 and 4. It drove for a little while fine then it misfired again. So I bought the wires, went to change all those and noticed that my 2nd coil and wire where different. It was short with no deep well compared to the 1,3 and 4 coils. So I took one of the old coils I pulled and replaced the 2nd coil. Finished changing my wires and went for a test drive. First thing I noticed is my car is now shaking hard while i sit holding the brake in drive or reverse. However if it sits in park, or as soon as I am on the gas the shaking stops. I drive for a day with no misfires. Until I stepped on the gas a little on the high way. This time it is a 1st cylinder misfire. Ok, that tells me i put a bad coil on. So I decided to buy 2 new coils for 1 and 2. Drove maybe 5 minutes and bam! It's back. So I need some suggestions on what else to look for to fix this misfire.
Now for the power steering. The light would come on, no power steering, so I found link to clean the connectors. I was hopeful this would work, due to it would come and go. Sometimes I could just turn my car off then back on and everything would be fine, or I would disconnect the battery and it would work. So I just finished cleaning all the connectors. I did notice the white on was very green and corroded compared to all the others that looks fine. So I scraped it with my knife while still spraying clean on it. I went and put all the grease on them and plugged them back. Didnt work. And now it smells, I'm hoping that is just a temporary thing and will burn off soon?
Lastly there is a loud rattle under the front passenger, I have looked and haven't seen anything that stands out. I know theres not much to go on for that one, just annoying and has recently started.
Also, rough idle too, it goes just over and under 1000rpm, sometimes it will die, or come very close. It has not died in prolly over a week. But I would still like to make it stop.
I can do most anything to fix what needs to be done, and would prefer to do it myself. So any suggestions would be great! Also If anymore information is needed just let me know.

If it misfires when you rev it out, I would take down the catalytic converter and examine the inside. The rattle you describe coupled with history of bad coils and misfires at high rpm all point to a clogged cat.

The shaking is a bit more unusual, I would make sure the correct coils are plugges into the correct spark plugs, and examine motor mounts for wear/leaking oil.

Replace all of the coils at one, not just one at a time. Make sure you use a quality spark plug wire set. I prefer NGK wires and I hope you are using the correct NGK plugs.

Along with removing the catalytic converter and checking it for breakage and clogging, inspect the engine mounts for signs of leakage. Degraded engine mounts can cause a heavy vibration at idle.

The loud rattling could be a loose exhaust heat shield. Inspect those while you're under the car.

Often times, cleaning the power steering harness does the trick but you will also want to make sure you clean the contacts on the rack itself. Ensure you are using an electrical contact cleaner. I wold also test the harness for continuity to ensure there is no corrosion present under the shielding.

All coil must be replace in the same time.After replace coil you should check your spark plug.Misfire should gone.