The original shifter i tried had multiple clicks so it could be trimmed.
All the new ones for 3 speed are 3 position. i bought a second one off amazon after having issues with the sram - was supposed to be non-indexed but it has 3 positions/clicks instead of being friction or having multiple clicks for trimming.
I don't know what crankset it has and the info off on the derailer is faded off. Likely cheap generic junk.