Have you guys ever bought a proxy? If yes, can you please tell me how to check a purchased proxy for performance and reliability? Are there any special tools for this?

Of course, on the Internet there are a lot of various tools that will help you to verify a new proxy. Personally, I use this proxy checker, which allows you to identify and find among many options really reliable and workable servers absolutely free of charge - https://proxy-best.com/free-proxy-checker/. Try it for yourself.