How many variations does the French horn have?

There are three valves on a French horn, excluding the thumb valve, which of course makes four valves.

3 valves on a single 4 on the double(3 valves and 1 thumb key)

normally 4 sometimes more but in all professional orchestras, 4

The horn consists of about 12-13 ft

yes, there are different wraps, different bores, different metals, different bell sizes, single, double and triple horns, and all horns have a different feel to them