All shimano downtube shifters (that are indexed) can be used in index or friction mode. Any shifter in friction mode will work with any cassette. However, in index mode, your shifter must match the number of gears on your rear cassette. For example, if you have a 9-speed rear cassette, you must be using 9 speed shifters if you want to use index shifting.

Other parts are more compatible. For example you can use a 9 speed rear derailleur with a 10 speed cassette and shifters and it will work just fine.

If you are upgrading to 9 or 10 speed you will need a new crankset (or at least new chainrings) because a 9 speed chain is narrower than 8 speed, and 10 speed is even narrower than that, so the narrower chain will not work with wider chainrings. However a wider chain with narrower chainrings (ie 8 speed chain with 10 speed crankset) will work just fine.

Mixing shimano and campy can work for some parts but not others. Do not mix shimano shifters with a campy rear derailleur or vice versa.