His uncle had a *wittygreat* idea: "You should get a driver's license, it will give you moreincrease your chances tof getting a job", he said.

We don't tend to call ideas "witty", we would probably say "great idea" or "brilliant idea". "give you more chances to get a job" doesn't sound right so I suggested an alternative

Unfortunately, on the first day Peter drove over a *sewer*, *prickunctured* onea tire and almost had an accident.

A preposition is almost always needed when talking about time: "on the first day", "at 9:00" etc. Pricking suggests sticking a needle (or needle-like object) into something but it obviously takes more than that for a tire to rupture, so a more forceful word like "punctured" is used. You would only ever say "one <object>" to emphasize that there is exactly one object, but that's not what you are doing here, so you can just say "a tire".

But after several months he couldn't find anyone.

"Any" is used when the antecedent is plural; since you said "job" in the singular in the last sentence, "one" is better here.

His uncle had a *witty*bright idea: "You should get a driver's license, it will give you more chances to get a job", he said.

"witty" is mostly used to describe clever jokes or writings, "bright idea" is the most common set phrase for expressing this concept

Unfortunately, the first day Peter drove over a *sewer*, *prickmanhole/sewer grating, punctured* one tire and almost had an accident.

"Sewer" is used to describe the entire piping system, it sounds weird to say he drove over a sewer when his tire must have been damaged by a "manhole" or possibly a "grating" that is part of the sewer system. "Pricked" is mostly used in the context of minor injuries to the skin I would say, e.g. you can be "pricked" in the finger by a sewing needle, causing your finger to bleed. Tires on the other hand are usually said to be "punctured."