#2
On the piano it means you play the quarter note with one hand while the other rests before it continues playing its part (in this case, the same cleff).
#3
I've seen it for guitar too - often when fingerpicking. Means the same thing. The bottom note shows the bass line - often played with the R H thumb. While the RH fingers play on the higher strings. It means the bass line makes a quarter note rest. (assuming you're right handed).
Si