I don't particularly like cross-overs, nor do I know anything about Invader Zim aside from what you explained, but I gave your work a look over, since you wanted some feedback on your writing.
Your descriptions of the characters are really cute and silly. They do a good job letting the reader know the basics of the character without adding excessive backstory.
The first part of your story seems to be... I'm thinking the fall of Earth, although it's a bit loony and anticlimatic, which may or may not have been your intent. The second part is Zim reporting his success, but his authorities send him on another wild goose chase in an also silly fashion. Lastly comes the part where you establish Twilight Sparkle's current agenda, although one thing I am missing is the setting. Is Twilight in her Library or in Canterlot? If she is in her library, does she really have servants there? If she does, would she really order them to message her back and read her books? It seems a but un-Twilight-like, considering her relationship with Spike, who already does whatever she wants for the most part. Just take that into consideration.
Other than that, it was fairly amusing to read. You are aiming for humor, I'm pretty sure. I do appreciate authors attempting humor and you don't do a bad job at it.