OK there will be two main issues causing this:
1) the only time the plectrum should ever make contact with the string is
when you pick the new note. If the plectrum is against the string
before you pick a note, the sound will cut off. These 'mini silences' are what makes a begginer's solo sound like a beginner soloing i.e. everything is disjointed and almost like a 'stutter'.
Practise making sure the plectrum isn't resting on the strings between notes.
2) When holding a plecturm, you shouldn't actually squeeze it. Your fingers should just support it rather than 'hold' it, if that makes sense. If you squeeze the plectrum, you will get a 'twang', as there is too much pull when you are picking. You will also end up doing step 1 when you squeeze the plectrum too tight.
To practise fixing this, support the plectrum between your fingers. Then ping it with your other hand. It should spin around or fall out of your hand. If it doesn't move, you are holding it too tight.
Try pushing down on the tip of it - if you are holding it 'loose', your thumb should move up. If you are holding it too tight, the plectrum will bend. This is bad, and what you want to avoid when making contact with the strings.
PS there is much more to this issue - but it always amazes me when players try to play fast/solo and don't know these things - the absolute basics. Try working on them and see how you get on. Like I said, there is more to it, but fix these things, then let me know.
-EDIT- sorry i'm just reading through everything in this thread. If you mean background noise i.e. sympathetic string vibration, then this is a different issue completely to the one I addressed lol
![Smile :) :)](https://cdn.jsdelivr.net/joypixels/assets/8.0/png/unicode/64/1f642.png)
But it is still worth trying what I said and making sure this is under control, as it could be a combination of these things.