More of a Game Graphics than a mechanics question

However, I have another question: what about just 45 degree to 90 degree rotations? Maplestory weapon sprites I've looked at so far are mostly at 90 degree (or multiples), 45 degrees (or multiples) (with the exception of 1h sword ones, which have alternate 'side view' sprites). Also there're the odd standing animations with something like 120 and 140 degrees. Considering just these three positions however, would it be possible to build a 90 to 45 or 180 to 45 degree algorithm?

An algorithm to do what, exactly? I don't understand what you're trying to do.

And what about somersault kick? I always wondered how they rotated your sprite when doing that skill.

Somersault kick only has two different character frames during the actual attack. One looks to be the "float" or "fly" animation while the second is one of the weapon swing or stab ones. The first has been flipped 180 degrees while the second has been turned 90 degrees.

Rotating a sprite to any multiple of 90 degrees should be pretty trivial. Hell, Microsoft Paint has done it for over a decade, no problem.
Photoshop is just over thinking it.

Also I have doubts as to whether they actually use vector graphics, vector graphics tend to become anti-aliased (but retain high quality) when zoomed out of. MapleStory sprites almost always have consistently black lines with little to no sign of anti aliasing (with the exception of the colors inside).

I have no idea how efficient converting to a raster version of the images would be, but they can always clean up any sprite versions and add those solid lines.
Since they're converting to relatively simple images anyway, they probably don't even use anti-aliasing.
I'm more of the opinion that the images begin as hand-drawn anyway. Just presented vectors as an option since I know that's how some developers do/did it.

It's just highly unlikely that they're hand-crafting any of the sprites in the game.
It takes too much time.