How is anyone allowed to make their own USD (or any forms of fiat for that matter) of any currency?
Because this is a free market, so anyone can make their own coin/token here.
Is there a method for doing this?
You could do it yourself, or hire some experts to create it for you.
Couldn't i just create a ERC-20 token and mint myself 1B tokens and use that to buy up the coins in circulation if i wanted to?
How would you get it on exchanges or let people use it as a USD Pair?
It's more to that, you can create yes, but being a stable coin, you need to prove that you have enough 1:1 backing of it and not be running on fractional reserves.