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You have to buy the rims from GM and the biggest size is 22'' rims more then that you will damage your Avalanches' chassis.
What are they rubbing on? If it is the control arms, you need a spacer between the hub and rim.
anything will will fit with modifications..
Yes as long as you run on the rims
yes as long as it is not rubbing anywhere
yes
4" lifts.
No. 22" rims will rub and scrub. You will need to do downsize a bit there.
18 inch rims will fit on your 2002 Cavalier. Any rims bigger than 18 inches will get against the wheel well.
Yes
yes.
Yes they will with no rubbing an you dont even have to lift it rims will go on an you wont even notice the difference