One common theme is the struggle of identity. When Percy is brainwashed, he loses a part of his true self, and the story often focuses on how he can regain that. Another theme is friendship. His friends have to figure out what's wrong and save him, showing the strength of their bonds.
One plotline could be that Penny is hacked by an enemy and turned into a brainwasher to manipulate her friends in RWBY. This would create a lot of internal conflict as the team tries to figure out what has happened to her.
One possible place to start looking for such fanfiction is Archive of Our Own (AO3). There are often a variety of unique takes on RWBY characters in fan-created works there.
I'm not sure about a specific widely - known 'Percy Jackson brainwasher fanfiction' title off the top of my head. But in general, in such fanfictions, you can expect to see a lot of character development. For example, Percy, who is usually so strong - willed, is suddenly in a vulnerable state due to the brainwashing. This can lead to interesting relationships with other characters, like Annabeth having to step up in a different way to save him. Fanfiction writers often use this trope to explore different aspects of the characters that we might not see in the original books.
The reason the cartoon kid is screaming might be that they are playing a game and got really excited. Another possibility is that they are in a dangerous situation and are trying to call for help.
Funny zoomed in faces cartoons are known for their focus on specific features like a goofy nose or a huge tongue. This emphasis creates a strong visual impact and makes you burst out laughing. They might also play with perspective to add to the humor.