It's like the Birthday Paradox. The chances that someone in a room shares my birthday are small, but the chances that two people in the room share a birthday is large. It just takes a few of the millions of tweets to go viral.
I won't address your second point at length except to say that it's naive to think that with the ease of broadcasting, suddenly the wall is at rebroadcasting, which can be done with no more than a click and is significantly easier than creating the original message.
It's like if someone in the early 20th century took random excerpts of someone shouting on a soapbox at an intersection, but published it on the front page of a national newspaper unfiltered. I'm pretty sure no one back there would have seen much value in doing that.
The life of ideas and clichés is largely independent of celebrity - if it hadn't been one twitter star that picked up some pithy arrangement of words that fit the zeitgeist, it probably would have been another.
The trying really hard part is just to be in the middle of things, and if you're successful at that, when you're the 1 out of 100 people who said the same thing, you're the one that gets the credit because you have 2M followers.
Thee fact that 99% of Tweet are irrelevant doesn't abnegate the fact that millions of Tweets from 'nobodies' are broadcast daily and do impact the world.
Journalists decide on an editorial angle and chose random tweets to support their narrative.
Entire articles are written on random tweets.
You don't remotely need to be 'famous' to have massive social media impact.
In a civilization of self-seeking individuals, the objective of communications will be self-aggrandization there's little incentive in promoting the truth.
The point of having professions is the expectations that the professionals will be, well, professional.
In reality, while it is easier to broadcast your message to people all around the world in modern times, people still need to "really believe in an idea to help it spread". Unless you're already famous, just because you put it on a platform with potential millions of viewers doesn't mean that you'll actually get millions of viewers without trying really hard.