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Key signatures essentially just indicate (or dictate) what the tonal center is, what notes are in the scale that you can pick from, and it all affects the overall flavor.
It sounds like what you are talking about is the difference between consonant (pleasant) and dissonant (harsh) intervals of simultaneous notes. Dissonance is not prohibited by any means, and can add color and flavor.
“Sounding good” is as much an art as a science, and while there are general rules, most can be bent or broken. Often, the dissonance that can come about with mistakes can improve the overall experience. There is a very old concept about it (I’m paraphrasing): “If you screw up once, it’s a mistake. To fix it, just repeat the mistake. They’ll think you meant to do it, and you’ll be considered a trail blazer.”. The short form of this is: “Screw up once, it’s a *mistake*. Do it twice, and it’s *Jazz*…”
For more information, your Google search terms should include “Learning Music Theory”. There are free tutorials that will help explain the mechanics of all of this.
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