I want to make this Social Network-ish thing, and I want user profiles to be located at www.mywebsite.com/[profile-name], but the thing is that I don't know how to do this. I can't use Laravel or anything like that. Only PHP.
Here are some solutions I came up with, but I don't know if they are possible or how to actually make them into code:
Larasvel is build using PHP ;) If you are going to build a social network solution, it is strongly recommended to use an established framework like Laravel, Yii2 etc. Why? Because it has tons of out of the box functionality you can use.
That said, you need to learn how to use PHP routing. Here is one solution. http://blogs.shephertz.com/2014/05/21/how-to-implement-url-routing-in-php/
Here is another routing solution: https://longren.io/basic-routing-in-php-with-altorouter/