I am going to start speedrunning from my PlayStation, do I have to stream and then use an overlay on my computer or can I just use my phone timer and submit time when I submit a run. Also is it compulsory to upload a run to YouTube or can I just submit a run on here?

Having a timer on screen is rarely required for submissions. Check the rules for the specific game and category to want to run to confirm. Mods will generally retime your video anyway.

This site doesn’t host videos; you’ll need to upload them somewhere else. YouTube is most common.

Generally the reason people use a timer is so they know what their own time is (to know when to actaully submit their run). Streaming is never required for running, you can 100% record it privately, and I also recommend youtube for hosting runs (and if you don't want many people tos ee them you can have them as unlisted youtube videos). Generally the requirements are specified on the leaderboard, but most boards require at least video with audio as a preference (and if you're gonna record with your phone or something, make sure the screen glare isn't too bad).

If you're new to speedrunning, welcome! And here's some FAQs that might help you: https://www.speedrun.com/speedrunning/thread/pt010