One day, after I filled the tank, the needle kind of tipped over. This is how it looks when the car is off:



And here is when it's on:



I'm not sure on what caused this, or how to fix it. Can you guys help me out? It'll go down a bit when the car is off, but the last 2 days, it has stayed around those areas. Let me know please> Thanks in advance.

At least you'll never run out of gas

I'd make a junkard run and just replace it. Plenty of others have expertise on the 00-05 clusters but usually the best option for a malfunctioning cluster is to replace it.

If it's only the gas gauge malfunctioning, I would first suspect the Sending unit in the tank.


Alont

I think it's definitely the cluster - especially since it's still messed-up when the car is off.
From what I've read, you should just be able to drop in a new cluster and maintain your proper mileage. That info is stored in the BCM if I remember correctly. The odds of you getting that one gage to read correctly again are pretty slim - unless you replace the gage itself which I would guess is soldered in. It would be a lot less work to just change out the whole thing.
I also believe that you could change it with a cluster from a Sunfire with no modifications, if desired. Just something to keep in mind if you would like a slightly different look. I've always liked the larger gages in the Pontiac cluster - it just took a while to get used to the orange illumination.
It would be good if you could find a wrecking yard that would let you take the part out yourself. That way you could get some practice before working on your own. I think that the Cavalier takes a bit of work to get in there, so it would probably be worthwhile looking up the procedure first before trying it. I don't think it should be too difficult a job - just a little time consuming until you figure out how its done.
John