Is It okay to upload a video of a IL to YouTube if the music doesn't sound, I mean like are there any copyright problems or do I need any permission?

You dont need game audio. If you do have game audio on, Nintendo is just most likely gonna demonetize your video, nothing else.

OK, thanks for answering, also, does a IL World Record count for something?

Speedrun records overall don't really count for anything. It's self improvement and competition that's the main point. For ILs, if the time is good, you should be satisfied, but they're not as competitive/challenging as full game runs so they have less value in my opinion. I gathered a lot of the IL WRs at one point for fun and yeah it's not something I could really brag about.