Yep, Stardust is useless against Desperado deck which can destroy multiple times per turn, as Stardust can only negate destruction once per turn due to its effect causing it to leave the field.
Plus, that's assuming you can get Stardust out in the first place.
Desperado’s multiple destructions happen at the same time, so yea Stardust would negate all of them- If you can put it out on the field and not get destroyed by battle
Again, Spider and Desperado combo easily stops Stardust.
I activate Spider's effect targeting Stardust, you're forced to activate Stardust's effect. Since Stardust's effect destroys, Desperado can be Special Summoned into the field.
Now I have Desperado on the field that can destroy the rest of your cards and hit you directly while you don't have Stardust since you removed it to negate Spider.