Does a guitar tuner work on a banjo?

Yes, but remember a banjo is not tuned like a guitar.

D - 1st string

B - 2nd string

G - 3rd string (one octave lower than the 5th string)

D - 4th string (one octave lower and the 1st string)

G - 5th string (the short string on top when holding the banjo)

A tuning fork (A) should do it, or you can find some good online tuners for guitar, banjo, fiddle, mandolin, etc. If you own and play an instrument and want a fast way to tune up, get a tuner for your instrument. But a tuning fork is probably the most versatile, if you can tune from an A. I've used the piano, and a melodica (mouth organ, yeah, yeah, I know, lol) before I broke down and bought a 10 dollar tuner that I could carry in my guitar case.

Yes, a tuner will work with anything that hits the note within the range you have it set to..

Yes.