what programming languages should I learn
First, the basics: HTML, CSS, JavaScript. You can never go wrong with them when you are in a browser. Keep them all vanilla and only add frameworks as an extra on top! You definitely should replace JavaScript with TypeScript (TS is a superset of JS, so you will need JavaScript anyway!), because types are a huge help to prevent many errors effectively and establish a better documentation in-code, enforced by the transpiler. It might also be nice to move number-crunching into WASM, for which you can use a range of languages, like Rust, C++, Kotlin,... however, I recommend Rust for various reasons I already explained a lot here on Hashnode.
If you want to use a game platform, then you might decide to use Unity, which can build for the browser, but requires C#. It won't help you build the website around the game, though ;)
What are the advantages and disadvantages of making my game open source
The advantages are, that you get help and feedback from other people, which includes coding, debugging and documentation by others. Also, GitHub and other git providers usually offer a range of additional tools which help you manage the project (like a Kanban task board, issue tracking, CI, etc.).
The con is, that you cannot really sell the game. You will have to provide additional services, like hosting an official server, offering additional in-game items, etc. Doing a Patreon might be a good idea, too!
Little spoiler: I am working on porting my Game-from-scratch article from Rust to web-dev and continue both, Rust and web-dev, in parallel. You might be interested in reading that, as I start simple and will introduce different aspects and mechanics (I won't write them as language tutorials, though). I will go for TypeScript as main language.
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Marco Alka
Software Engineer, Technical Consultant & Mentor