I see them on Ebay advertised to fit 96-01. Why? I also notice even the 01 A4s used 205/55/16 tires rather than the 215/55/16 tires installed on my car.

5 lugs are easy to see with the naked eye. I know I want 16" diameter. What is the difference between a 16 x 7.5 and a 16 x 7? What is the offset number? Are these numbers marked on my spare somewhere? Thanks!

B5 ('96-'01) had 205/60/15, 205/55/16 or 225/45/17 stock.
B6 ('02-'--) has 205/65/15, 215/55/16 or 235/45/17 stock.

If you're looking for 16" rims, you should be running a 215/55/16 tire, and for that either 16x7 or 16x7.5 rim will work. 7.5" rim is half an inch wider than 7" rim, but they both are 16" in diameter.

As far as offset, anything between ET35 and ET45 will work. The stock audi 16" rims are ET45. If you get ET35, the rims will be sticking out 10mm further out, which looks a little better, IMO, as they will be more flush with the wheel fenders.

As far as bolt pattern, of course you need 5x112. All 16" rims from the previous generation A4 (B5) will fit your A4 as well.