The hose is just a way to burn up noxious vapors emanating from the crankcase by routing them back into the carburetor (where they are sucked into the combustion chamber and burned up).
The screw your brother messed with is the likely culprit. Most likely a mixture screw.
You know, it's not a bad idea at all to photograph the engine on a new kart in explicit, painstaking detail as a record of sorts. Therefore, when things fall off or are messed around with, you will know what it was since you'll have a photo of the engine in "as-bought" or "once-working" condition.
In the meantime, tell your brother to buzz-off.
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