How is anyone allowed to make their own USD (or any forms of fiat for that matter) of any currency?
Anyone can launch their own coin or token with whatever properties they wish. If you want to launch a coin and state that it is pegged 1-to-1 with a fiat of your choosing, you are free to do so.
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?
You can absolutely create a token out of thin air and give yourself 1 billion tokens. Many people have done that in the past. The harder part is convincing other people that your token is worth anything. You can't just "buy up" other coins unless someone is willing to sell them to you. If all you are offering them in return is some useless token you have just created with no infrastructure, development, product, or future, then you are going to struggle to find people willing to trade with you. It would be like if I wrote "IOU $100" on a slips of paper and tried to buy groceries or pay my bills with them.
How would you get it on exchanges or let people use it as a USD Pair?
Start a company, hire a team, develop your coin, prove to independent auditors that you are holding enough assets that it is actually backed up 1-to-1 with fiat as you claim, set up a platform to allow users to cash it out for fiat, maybe start your own exchange or get it listed on some small exchanges, and work up from there. Good luck with that.