You're a non-trader. So you maybe don't even 'get' what short-selling is intuitively yet. Let alone options. I'll try to make this as simple as possible.
Stocks first, options later:
Let's pretend we're not trading stocks, we're trading the latest Playstation 5 (seems appropriate).
If you think the price is going up then you buy a PS5 today, hold onto it, and hopefully sell it for a higher price in a few months.
If you think the price is going down, then you short-sell a PS5. Which goes like this:
You find a mate who already has a PS5. He's not really playing it right now. So he offers to lend it to you for £5 a week, as long as he can have it back as soon as he decides he doesn't want to lend it out anymore.
You sell the PS5 today for £500. And hope that it drops in value fast enough that when you have to buy it back, you'll have made a profit on the whole thing.
The key elements are that you have to borrow it from somebody who already has one, you have to pay them something (usually it's interest, not a fixed charge), and you have to buy it back later, sometimes without any say in when that happens. (Unlike with your actual mates, brokers and clearing houses aren't going to give you any leeway when they need to recall the shares).
Now if you sell too many like this, you might not be able to find enough to buy back when the time comes, and will be forced to pay whatever it takes to get them.
If somebody (In this case, people on reddit) notices that you've sold all these Playstations you don't have, they might decide to buy them all up first, to make sure that there are none left for you, and you have to pay an exorbitant price to buy them back.
This is a classic short squeeze. And usually you'll end up buying the Playstations back for 50%, 100%, 200% more than you sold them for just to get out of the trade.
That's bad enough. But now enter options:
Today, we're just going to talk about call options. A call option looks like this:
I pay you some amount of money for the option. In return, you promise to sell me 1,000 Playstations, for £2,000 each, at any point in the next 3 months, if I decide I want to buy them. (I have the option of buying them at a fixed price. Hence the name).
Back when Playstations were going for only £500 each, hedge funds would happily sell you that option for almost nothing, because there's no way the price is going to go that high in the next 3 months, so it's basically free money to them.
But then here's what happens:
They sell you a huge pile of options. In fact, they sell you options for half of all the Playstations in the world. Because there's no way they'll ever have to actually deliver them.
Then you start squeezing the stock. The price goes from £500 to £750. The hedge funds start getting a little nervous. £2,000 is still a long way away, but the price is already higher than they thought it would ever go. So they buy some Playstations just in case.
But buying more Playstations pushes up the price even further. Suddenly they're at £1,000 each. The hedge funds and the short sellers are starting to sweat a little. They buy more Playstations.
The price is pushed up even more. So they panic even more. And buy even more. If there's enough people buying because they sold the shares short. And enough people buying because they sold options they never thought would ever have to be fulfilled. And not enough Playstations to go around because the guys on the other end of this trade already bought them all, and all the options, and are holding them ransom.
Then there's nothing stopping the price going to infinity. (Or in this case, going up 2,000% and counting). *
The people who sold the options. When they buy a little bit to hedge. And then start buying more and more as the price gets closer to the point where they're on the hook. That whole thing is called Delta Hedging, and the amount they buy as the price changes is called Gamma (and hence this situation would be called a gamma squeeze). It's just "buying more of the thing you're on the hook for, the more likely it is that you'll actually have to deliver it".
Now to answer your questions:
Yes, if you buy the shares. And keep holding out for a higher price. You might miss the window as the whole thing comes crashing down again. Because it will crash eventually. Options will expire. People will decide to cash in and relieve the pressure. At a certain point, often quite suddenly, the whole thing will go into reverse and it'll be the people holding the options and stockpiling the Playstations who are desperate to dump them before the price crashes even further. Maybe you're the guy who buys the shares at $20 and sells them at $60. Maybe you're the guy who buys them at $60 and sells them at $300. And maybe you're the guy who buys them at $300 and sees them crash to $100 only an hour later. **
As for the $50,000. That was a guy who bought those options for pennies on the dollar. Basically the funds went "Yeah, sure, Playstations at £2,000 each within 3 months. Never gonna happen. We'll offer you 200:1 odds on that". He bought them, it happened, and now he can cash it in for a massive payout.
The way that actually works is that the option is for 1,000 Playsations at £2,000 each. And they sell the option to you for £2,500 total (£2.50 per potential Playstation). So you buy 20 options for £50k.
They're worthless if the price is less than £2,000. But if the price is now £3,000 per Playstation (IE your £2.50 per console is now worth a cool £1,000 per console). Then they're worth 1,000 Playstations * £1000 * 20 options = £20 Million, for a 400x return.
* There are, actually, lots of things that will eventually stop it going to infinity. If not people selling of their own accord, then brokers or regulators will eventually step in and put a halt to things. In this case, brokers just stopped most retail traders from being allowed to buy new shares/options, which stops the squeeze and starts the rush to the exits.
** Like, say, today. 28th January 2021. Where GME opened at £263 per share. Almost doubled in the space of 30 minutes to £469 per share and in the 90 minutes since has dropped 75%.
If you enjoy entertaining and informative explanations of what the hell is going on in finance today, you should read everything Matt Levine has ever published. Including the last 4 days' coverage of GameStop.