🤔
What penalty if you are adjusting your pieces on your opponent time ?

Stop the clock and notify the arbiter. He can warn the opponent for the first time and afterwards award you two minutes. In time-trouble even instant punishment, 2 minutes. Same for j’adoube not having the move.
I cannot recommend self-justice like pressing the clock back which can be interpreted as nullmove e.g. illegal move. Look into relative new FIDE rules.

Well you know most of the time we are bound by common standards of decency between players. If we were just bound by rules enforced by arbiters then chess would be impossible.. I would just tell the player to adjust when it was his turn if he did it more than once. If he did again I would stop the clock and call an arbiter.
Perhaps there is more gamesmanship in Russia ? Anyway, let me tell a true story of unbelievably bad sportsmanship during a club game her in Birmingham England in the last two years:
Two very strong players were down on time. One player was likely to queen his pawn very soon. One player saw that time was short and gathered both spare queens close to himself.
When the other player pushed his pawn to the eighth rank HE THREW HIS OPPONENT'S SPARE QUEEN TO THE OPPOSITE CORNER OF THE ROOM !!!
The player that did that was Russian. Apparently he got the idea from a master game when the same thing was done. So, perhaps trying to work round the rules and aggravate the opponent is common in Russia? (BTW I'm not on the Libtard "Russian bashing bandwagon" and watch RT for news.)

No. If you release the piece you‘re not having the move, strictly speaking. Even if your clock is ticking. But in praxis this should be still ok.

I have no problem with piece fiddling as I try to put the position in my head.
I hate pieces that are part on another square though.

6.2.5 is clear ...only the player whos clock is running is allowed to adjust the pieces.
Penalties are discretionary though so many time life in prison isn't the sentence issued.

FIDE 2018:
1.3 | A player is said to ‘have the move’ when his opponent’s move has been ‘made’. |
4.2.1 |
Only the player having the move may adjust one or more pieces on their squares, provided that he first expresses his intention (for example by saying “j’adoube” or “I adjust”). |
As I told you adjusting shortly after your move is more or less tolerated usually.
I'm talking about OTB of course.
One of your pieces fall down on a chess board, you hit the clock button and only then adjust your piece(using your opponent time).
I asked an IM arbiter another day and he said nothing happens even if you call an arbiter !
I strongly disagree I think some punishment MUST follow, especially if you keep doing that more then once or twice during a game, especially blitz where time is pressures.
What do you guys think ?