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I'm just wondering, does the difficulty increase every time you complete an episode? Also, does the high score list incorrectly show the next difficulty level you'll be at (rather than the one you played that episode on)?

In most games, I would think that the difficulty you choose would stay that way permanently, but maybe not here. In fact, I played through the whole game once starting on hard and just made that assumption (and I never looked at the high scores), but I since have reinstalled the game and don't have any of that save data.

Here's what I'm seeing:
After completing episode 1 on hard, it shows up in the high score list as "insanity". (I guess that could be "Impossible" difficulty....) When I completed episode 2, it said "Suicide" (definitely a difficulty level). Just to see if I was crazy, I quick ran through episode 1 on easy and it shows up as normal.

Is this normal or did I somehow make the game far more difficult for myself? (I'm not sure what I would have done....)
Alternatively, is the high score table just plain wrong or is it noting something else entirely, e.g. score ranges?
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Good catch noticing this. I just checked my copy of the game now, and it appears to be a glitch with the high score lists, because I got the same result as you. Specifically, I played the game on normal, and the high score for episode 1 says "hard", the one for episode 2 says "impossible", the one for episode 3 says "insanity", and the ones for episodes 4 and 5 say "suicide". I'm sure I was playing on normal difficulty the whole way through, because it struck me while playing that the difficulty did not ramp up in later episodes to keep up with my ship upgrades, resulting in episodes 4 and 5 being laughably easy.