Today, I read a few articles onin the New York Times and broadened my vocabulary. Today, I read a few articles in the New York Times and broadened my vocabulary.

Today, I read a few articles onfrom the New York Times and broadened my vocabulary. Today, I read a few articles from the New York Times and broadened my vocabulary.

I've once knownew an arrogant, pompous man who never talked to hard-working people from his neighborhood, because he always thought he iwas something better. I once knew an arrogant, pompous man who never talked to hard-working people from his neighborhood, because he always thought he was something better.

“Once” here is referring to a time in the past, so the present perfect shouldn’t be used.

I've once knownew an arrogant, pompous man who never talked to hard-working people from his neighborhood, because he always thought he is something betterwas better than them. I once knew an arrogant, pompous man who never talked to hard-working people from his neighborhood because he always thought he was better than them.

I've once known an arrogant, pompous man who never talked to hard-working people from his neighborhood, because he always thought he iwas something better. I've once known an arrogant, pompous man who never talked to hard-working people from his neighborhood, because he always thought he was something better.

To his dismay, he ended up working in a local factory owing tobecause of his frivolous mannerway of life. To his dismay, he ended up working in a local factory because of his frivolous way of life.

“Way” makes more sense to me both because “way of life” is a set phrase and because I would expect “manner” to refer to an action. I changed “owing to” because the pacing didn’t sound right to me (I expected a pause before it) and because I tend to see it used before the main clause that it modifies, not after.

“What a mesmerizing painting this is," he said with unprecedented enthusiasm. “What a mesmerizing painting this is," he said with unprecedented enthusiasm.

That's a vapid piece of nothing," she retorted while seeinglooking at a blue paper with nothing interesting on it. That's a vapid piece of nothing," she retorted while looking at a blue paper with nothing interesting on it.

That's a vapid piece of nothing," she retorted while seeinglooking at a blue paper with nothing interesting on it. That's a vapid piece of nothing," she retorted while looking at a blue paper with nothing interesting on it.

During this scorching summer, the villagers deplored the lack of water, which—in this parched area—can be deadly if properly unprepared for. During this scorching summer, the villagers deplored the lack of water, which—in this parched area—can be deadly if unprepared for.

During this scorching summer, the villagers deplored the lack of water, which—in this parched area—can be deadly if not properly unprepared for. During this scorching summer, the villagers deplored the lack of water, which—in this parched area—can be deadly if not properly prepared for.

“Properly unprepared for” could read as “not at all prepared for,” but in my experience, that’s only when it’s attached to a subject as a descriptor. Since that’s not the case here, it didn’t really make sense to me.

During this scorching summer, the villagers deplored the lack of water, which—in this parched area—can be deadly ifor those not properly unprepared for. During this scorching summer, the villagers deplored the lack of water, which—in this parched area—can be deadly for those not properly prepared.

I try to avoid ending sentences with a preposition.

During this scorching summer, the villagers deplored the lack of water, which—in this parched area—can be deadly if properly unprepared for. During this scorching summer, the villagers deplored the lack of water, which—in this parched area—can be deadly if unprepared for.

Therefore, people stow away in ships to flee to a neighboring country in order to hide from the incessant terrorism. Therefore, people stow away in ships to flee to a neighboring country in order to hide from the incessant terrorism.

"Terror" is like "fear", an emotion. One wouldn't go elsewhere to hide from an emotion. On the other hand, "terrorism" refers to acts that cause "terror", and fleeing from such acts makes sense. But some people may feel your sentence is fine the way you wrote it.

He's wavering between going to university andor starting his own business. He's wavering between going to university or starting his own business.

If he goes to the university, he might capitalize on his knowledge in his future career. If he goes to the university, he might capitalize on his knowledge in his future career.

This is fine, but I would write “the knowledge that he will gain” so as to make it clear that it’s not pre-existing knowledge that he already has.

If he goes to the university, he might be able to capitalize on his knowledge in his future career. If he goes to the university, he might be able to capitalize on his knowledge in his future career.

Your sentence is not grammatically incorrect. I just had to add "be able to" in order to make the sentence clear to me. :-)