Does the mixolydian mode / scale have to change with the chord changes ?
I played it in C major and didn’t change with the chords and it sounded good .
Thank you
If it sounds good that’s all that matters. Use it like you would any other scale, just listen out for clashing or unpleasant notes and avoid them just like you would with using a major scale in a major key.
When you solo with scales (or modes, which are just scales) listen to the chords and how they react with the scale notes. Most clashes will stand out when you hang on a note for more than just a moment. If however you are moving through the notes quickly and then resolve them, they generally go unnoticed, sometimes they even sound good. Hang on to a note and you get a different sound all together.
To understand this, play each note of the scale and hang on to it for a little while. Do this with each note over each chord and you’ll hear which notes to avoid hanging on to over each chord. You can learn a lot doing things like this.