I am programming my own game called War Of Cards and I want to make a category of speedrunning for it but I don't see any buttons like "make category". Can I do it at all? If yes - how?
(this game was published on my Google Drive: https://drive.google.com/drive/folders/1sIAV4hxoQExPGKTmgqhY5SgKi9RxwKC6?usp=sharing)

If you are asking about how to add your game to the site, you will have to request it (Read all the rules first):
https://www.speedrun.com/requestgame

I am also programming a game and wanted to add it to this page, but when I read the rules, there was written that the game dev is not allowed to add it's own game to this platform. But why??

I want to create a new speedrun for an already existing game, but idk how...

Yes, you can, but you can't create a category by yourself unless the game has already been added to Speedrun.com and has moderators.

I'm actually wondering something similar because I'd like to create a category for [Movers and Packers](https://moverspacker.ae/), but I couldn't find an option to do it either. From what I've read, the first step is to submit the game to Speedrun.com. Once it's approved, you (or the assigned moderator) can create categories and set up the leaderboard.

If your game is only hosted on Google Drive, you may also need to provide enough information about it during the submission process. Hopefully someone with experience submitting a new game can confirm the exact steps.