There are specs on Terry's website for an '02 Classic (look under "Bikes On Sale") but not an archive. Do you know whether they changed the bike between '02 and '05?

The number of teeth is stamped on the cogs, but they can be hard or impossible to read while they're on the bike. It'll probably be easiest to see the small chainring and, if you don't have a pie plate, the largest cog on the cassette. It shouldn't take you that long to count though.

You only have to measure the run-out of your tire if you're super obsessive. Tire and wheel size doesn't affect the ratios anyway, it's a constant in your equations. Top gear is top gear whether your wheel is 24" or 700c.

But really, unless you're racing and it's super important, just shift by feel. If you're not in a gear where you're in danger of cross-chaining, then shift the rear derailleur only. If you're in, say, your largest chainring and the middle or "low" end of your freewheel cogs and you want to downshift, then downshift the front and upshift by a couple in the back until your cadence and the amount of effort you're expending feels right. The cogs on the cassette are your close ratio shifts, the chainrings give you ranges. No one shifts back and forth constantly between the front and the rear to get an exact sequential progression of gears. It's not necessary and you'd waste a lot of momentum shifting.