Edit: he's probably not faking being "retarded" entirely, but he's playing up and exaggerating his condition
TLDR: Lil Kev overhears them calling him "retarded", then does all the laughing and unusual behaviour while watching cartoons, just to make them think he is "retarded", only to make them look stupid by doing his rap on stage
At 07:38, he clearly overhears Dennis and Dee calling him "retarded" upstairs in his house. At this point he's wearing normal clothes which have all been put on correctly.
Is it just me, or does he seem to act more "retarded" immediately, compared to his earlier scene?
Only after this, In the next scene, he's seen wearing his shirt backwards and doing all the unusual behaviour and the laughing. He's making Dee think he is "retarded"
He then does his rap to make Dee and Dennis look dumb, and prove that he is smarter than them after all
***
More context to the theory:
Maybe he does have some kind of condition which gives him learning difficulties. This is what Dennis remembers from school, and explains some of what his mother says about him. This is why he may seem a little unusual, and why his hand/finger movements did appear abnormal in the first scene - before he overhears Dee & Dennis.
However, he's been able to live a normal life and is intelligent enough to be a writer and musician. But he resents the stigma of his condition which has surrounded him all his life. Now the gang is stigmatising him as well, he wants to get back at them by playing up his condition and tricking them, proving he can outsmart them despite his condition, ie: "who's retarded now".