Can the leading note resolve down?

You're absolutely right! The typical rule is that the leading tone must resolve up to tonic when it is in an outer voice (that is, the soprano or bass). If the leading tone is in an inner voice, it can resolve down a third to the fifth of the tonic chord (a so-called "sprung" or "frustrated" leading tone).

1. Does the leading tone always have to resolve up?
2. When can you frustrate the leading tone?
3. What happens to the leading note in any minor key?

Does the leading tone always have to resolve up?

The leading tone should almost always resolve to scale-degree 1 except when “springing” a leading tone in an inner voice (see below). 3. In minor, the leading tone will need to be raised in order to use a dominant chord for cadences.

When can you frustrate the leading tone?

When ti is in an inner voice, it can progress down to sol if necessary to accomplish good voice-leading in the other voices and ensure complete chords. This is called a frustrated leading-tone. When ti is a functional dissonance of a tonic-functioning chord (see below) it should progress down by step.

What happens to the leading note in any minor key?

Answer: Usually the term "leading tone" is applied to the 7th degree in a major scale or the raised 7th degree in a minor scale. For example, B in the key of C, or G# in the key of A minor. ... A leading tone would be part of a dominant chord (the V or V7 chord, or the vii dim. chord that is almost the same thing).