I'm searching for a way to remove spells already casted if ever certain conditions are met in order to prevent them from hurting anything as soon those conditions are met.
If possible, give me an example with Psionic Storm.

I'm not entirely sure what you're asking... I'll teach you grammar for 50 minerals an hour and then help you with data editor stuff for 125 minerals an hour?

Edit: to take a stab in the dark, I would think you should look at Validators. They are basic If, Then, Else statements in data-editor format. I think Psi Storm checks periodically for units in an area to apply a damage buff to, but if they already have the damage buff on them then it is not applied again.

Something like Create Persistent>Search Area>Apply Behaviour (validator)>Damage

Not entirely sure how the apply behaviour fits into it since I dont have SC2 available to me right now, but I think the Validator checks for the Buff - since I remember units getting psi stormed display a buff on their unit portrait things.

Let's put it in a simple way: if I move a group of units to a certain locations, and there is a storm already casted at this position, I do not want the storm to damage the moved units.

I would still think you should look at Validators.

Or maybe an aura which removes the damage effect - nope. The damage effect is applied at the same time as the Buff. Turns out the Buff is applied only as a way to stop units already taking damage from one Psi Storm - ie. Storm damages don't stack.

Why do you want to do this anyway?

Edit: Create an ability which applies the Psi Storm Damage buff to your moving units. Or do it through the trigger action Add Behaviour.

Are you 100% sure this will prevent it from damaging units? Wouldn't it damage them even if there aren't any storm instead?