To your questions from easiest to hardest.

2. Yes, the clicks are the indexed positions built into the shifter and typically they're only compatible with parts from the same manufacturer for the same number of speeds.

3. In theory a friction shifter can work with literally any drivetrain - but in practice there are limitations because your shift lever may not able to pull enough cable to swing the derailer all the way through its range, and with 9 or more speeds the gap between gears may be so small that the shifting will be impractically finicky to use. Note that SRAM rear derailers in particular are not going to play nicely with friction shifters, as they require more cable pull per shift than other brands.

1. Derailers don't just vary according to 'speeds' as there are variations how much chain different derailers can wrap, and the derailer for a system with a given number of 'speeds' will be optimized for a particular set of chains and cassettes. If you wanted to use a 10-sp derailer with a 7-sp freewheel you'd need to use a 10- or 9-speed chain that would be narrow enough to fit through the derailer and this chain might give you some odd shift issues depending on which freewheel you were using, so given how expensive these parts are it would make more sense to use an old derailer and 7-sp chain instead.