Does this Sallen and Key filter work on a single supply and does the input offset matter?
The answer to both questions is yes. For a more complete explanation you need to redraw the circuit with component designations.

Continuing my answer using the new schematic. Although one usually sees single supply circuits biased at one half V+, the ideal point is actually midway between the output swing of the amps. A 324 typically swings between .5 and 10.5 volts, so 5.5V would be best ; which is not that much different than 6V. In this application one can make the source oscillate around the 5.5V point, so all that this circuit needs to be single supply compatible is a capacitor in series with R3. Then when you change the gain ( and Q), by varing R4, the output remains centered around 5.5V.

Making the resistors independently varible creates a huge range of issues that are too big to cover here. The best way to do this is to keep R1 equal to R2( roughly) and vary them together to change the center frequency of the filter. I think only Qs of more than one will be useful here. So if R3 were a more reasonable 10K ( and connected to ground through a 1 uF cap), then varing R4 from 10K to 20K would change Q from one to infinity ( at which point the filter becomes an oscillator.) Also keep in mind that changing the Q this way also changes the amplitude.
R4 is optocupler 3.