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How do you measure wheels to get correct size for replacement and then how do you know what is the correct size of tire to fit on new wheel?

I presume that you are looking for aftermarket wheels and tires to fit those. Most of the time you could be better off finding tires that are the right width and diameter and picking wheels to fit them. There are online charts available from Slot Car Corner, Slot.it, Professor Motor and others to match tires and wheels. If you have something specific in mind just post that, someone is likely to know a good combination.