If you look at a regular character sheet, you'll see there are 4 rows for the same character - each row faces a different direction. As you turn your player around while walking, to face different directions, it makes it use a different row from the spritesheet. The top row is what shows when you're walking down, the second row shows when you're walking left, the third when you're walking right (or vice versa - don't have one open at the moment), and the fourth row shows when you're walking up. On your damage sprite, you only have one row filled in. If your actor showed the damage sprite and you made them go left, right or up, the image would actually disappear. Only making them move down would have the correct image. Turning on Direction Fix makes it stop this behaviour - the direction that is currently being used is 'locked in', which means even if they move in a different direction, the sprite will not change to a different row.
Now look at the columns - on a regular character sheet, each cell in a column faces the same way, but they have different stances. The middle one will be "standing", and the ones on either side will have either the right foot in front or the left foot in front. When your character is standing still, the middle sprite is the one that shows. When they are moving, it alternates between the sprites, going from right to left then back again. This is called Stepping Animation, and it's turned on by default for the character and all NPCs. When you are dragging a character, you don't want it to display this motion, so you turn off Stepping Animation while dragging, then turn it on again afterwards.
What I can't figure out is why, after you'd done the move route and changed the actor to the 'down' position, did it change back to the walking sprite after you started moving again. It should not have. There is nothing in your event that would cause it to change back to the walking sprite.
Do you, by any chance, have any plugins that affect map sprites? Galv's Move Route Extras, for example? Or any that change the sprite based on whether you're idle, walking, or running? That would cause the sprite to change when you started moving again. The solution to that is to NOT use the actor at all, but to use an event with the actor's sprite instead, making the real actor transparent while the cutscene is going on.