UPDATE:
Ok, so thanks to the help all of you provided (again, thanks so very much) I was not only able to fix my animation issues, or at least, I've only directly applied the changes to one character, and then remade the rest practically from scratch, but I noticed what I was doing wrong.
It turns out I was using some pretty "hard" conditions to move characters around.
So, instead of using "On Moved", I kept using "If Platform is Moving", or instead of "On Jump", I used "If Platform is in the air".
These things completely blocked any attempt from me to execute any animation properly...
So, thank you! This was much help!
----
Now... could I ask one tiny more thing?
I decided to settle with just MIRRORing the graphic of the only character whom I wanted to have a separate graphic when he's facing left and when he's facing right.
But if any of you has the time, could you explain to me how you would do it? I mean, handling a character WITHOUT the SET MIRROR event so that he has small changes when he's looking at different directions?
I'd really appreciate that, but it's not SUPER essential. It's just that it's killing me that I can't figure it out.
I had managed something really close, but if I make him move to the right, and then move to the left (if I accidentally press the other way fast enough) the character will strafe backwards. And that will mess up the rest of the animations, such as jumping, etc.
Anyway, consider it a sidequest, perhaps. But once again, the main problem has been resolved, you have my thanks!
The easiest way is to use a global variable to keep track of direction a player is facing.
Global Variable Direction=0
On player facing Left: Set Direction=1
etc.