Here's my take.
a) The Elders didn't always want to take a trek to the Shed, so they also hid the suits in the houses for convenience sake. As for Noah finding one, Mr_Glass.1's explanation works for me. Noah wasn't unintelligent, he just had learning and articulation issues. Noah was a sneak, and the fact that he visited the woods regularly means he probably saw the "monsters" and figured out they were fakes. It's obvious he knew the whole thing was a hoax, considering he always cracked up when the creatures made noise or invaded the village. To him, it was all a joke.
Eventually, however, this brings him to a much more sinister conclusion: Evil is a joke.
He begins to think there is something funny about swatting younger boys with sticks, handing someone a symbol of evil (the red berries), and takes a peculiar delight in Lucius "getting in trouble."
This leads to question b) Why was Noah in the costume?
Noah wore the monster suit because he was evil. In his bitterness he gave himself over to complete depravity, and put on the creature suit to show his acceptance of the dark side of his soul. He decided to become an animal. He wanted to make Ivy pay for choosing someone else over him, and for rejecting him when he tried to take the life of his rival.
He put on the monster suit as an expression of his condition.