does it matter how far apart the electrodes are in the conductivity measurements?

Answer 1

Yes, since the electrical conductivity between the electrodes is inversely proportional to the distance between them. Or in other words, the resistance (resistance = 1 / conductivity) is directly proportional to the distance. Greater distance = greater resistance. This principle is generally true of conductors, e.g., a 200 foot length of wire is going to have twice the resistance (or half the conductivity) of a 100 foot length of the same wire.

If you're going to be using the same setup to measure the conductivity of several solutions, make sure your electrodes remain at the same distance so that you can accurately measure their relative conductivity.