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It is my understanding that subdominant chords, IV and ii, contain the fourth scale degree. The fourth scale degree wants to resolve down to the third scale degree. In the scale of C major (C, D, E, F, G, A, B, C), the F note wants to resolve down to E.

1) What makes a note want to resolve?

If it is because it is a half step away, (even then, I still don't understand why that makes it want to resolve), how come in a minor scale, the iv and ii^o scale degrees also have this tendency? In a C minor scale, (C, D, Eb, F, G, Ab, Bb, C) the fourth scale degree is now a whole step away from the third scale degree, not a half step anymore. What makes F want to resolve down to Eb?

By the same token, in C major scale, B wants to resolve up to C (half step). In this case why does Bb want to resolve up to C (whole step)?

Valid point about the subdominant to m3, but the leading note argument isn't strong. It's mainly because the B♭ in C minor doesn't push too well that the 'raised leading note' is used in far more pieces in minor keys.

It's probably not that the music 'wants to move in a certain direction' but more of what the listeners prefer to happen.

Music theory basically states what happens in music. If something is seen to work well, many times, it's noted (no pun), as something useful to bear in mind for the future. It's helpful to writers and players. Sort of if it ain't broke, don't mend it premise. Great writers tend to use phrases liked by the majority of listeners and players, so when they use certain intervals and directions of certain notes, those become accepted into theory. Why wouldn't they? But by no means does that mean the ideas become rules to follow.

Maybe notes are like electricity - they like to take the shortest route? The leding note generally does, but the sub-dominant going to M3 - possibly it goes the other way just as much.

When you refer to the IV and ii chords of major key as subdominant, you are using a field of musical analysis called functional harmony (video reference). As for the reason why notes like the 4th and 7th in major want to resolve, the explanation that I have heard is that both sit a semitone away from the notes of the root major triad, the 1-3-5. Further, the 7th is said to be the most directional because it sits right below the root, the most important note in a key.

Minor, on the other hand, is a whole different can of worms. In fact, in the common practice period, composers found that the chords build with the natural minor scale were so undirectional they invented the harmonic minor scale to solve that problem without having to change key. If you want to apply the ideas of functional harmony to minor you have to take some liberties. The author of the video which I linked has another one about exactly this topic linked here. To my knowledge, music theorists do not believe that the 4th wants to resolve to the ♭3rd or the ♭7th wants to resolve to the 1st. When you want to think of subdominant function in minor, look to the subdominant chords in the relative major key. The relative major's IV is minor's ♭VI and its ii is minor's iv. The main subdominant chords in minor are actually the ♭VI and iv. Usually, the ii^o in minor is considered to be dominate (and is played as a 7th chord often). In common practice music, the ii chord is also used in minor and can be considered subdominant.

It is worth knowing that functional harmony was developed around major. Sometimes, the ♭III or ♭VII are subdominant in minor. On the most basic level, what makes a chord subdominant is not its notes in particular, but the fact that it sets up the dominant chord.

I'd like to include a general note, which is something that I needed clarifying recently. There isn't any law of the universe saying that one note needs to resolve down or up to another or that it even can. Music theory is about giving structure and explanations to what is going on in music. 4ths going to 3rds and 7ths going up to 1sts or them feeling the pull to their respective note (resolution) is just an observation shared by many theorists and musicians alike. It may not be true for you, in part or entirely.

A note wants to resolve to another note because they're dissonant and close enough to each other that your mind conjures there will be closure (consonance) if the next note is a resolution.

It's kinda like a musical version of 'snap to grid' in a graphics app ... a natural 'magnetics of frequencies' occurrence.

Another analogy, and this is real, is cracking one's knuckles on all but one finger ... there is a 'ceiling tile' effect that the one 'unadjusted' knuckle stands out like a black ceiling tile in a football sized ceiling of white tiles.