You insist the question is not about Science, and not about Worldbuilding – since you've posted it here I will treat it strictly as a Writing question.
I was wondering if there were any resource that teach Quantum
Mechanic without the math well enough so that aspiring authors can
write realistic science-fiction books.
The best would be a video tutorial that doesn't cover the math aspect, is scientifically accurate, doesn't simplify thing and doesn't lead to false beliefs that you find out about after taking a real course on it (as much as possible).
How do I learn just enough (science) to sound like I know what I'm talking about, but nothing more? And also I don't want to have any false ideas from the gaps in my knowledge.
This is a Catch-22. There are no shortcuts. You must learn enough to know what you don't know, or you must avoid discussing it in-depth, probably both.
Since you give us no details, and no measure of "realistic", we can't tell you how much knowledge is enough for your story. Youtube is not a community college, but The Royal Institution has been hosting science lectures for over 200 years, and their Physics Playlist has great talks. Stick with accredited universities or legitimate science foundations.
It still begs a broader question: how to research science as a science fiction writer.
Typing "science" into the searchbar offers over 1000 results. Here are some examples from the first 2 pages:
Researching Future Technology for a Science Fiction Novel
Can a person get bogged down by science fiction research?
Rewriting a scifi story to fit with actual science, should I do it as I go?
When writing science fiction, how important is it to provide scientific details for the (fictitious) things you are presenting in the story?
In Science Fiction, how does one do research, but write at the same time?