Is it legal to hit the clock with piece, captured or otherwise? I have often seen in blitz games that when a player captures a piece and then hits the clock with the piece. Is that a legal move or is the player required to place it on the table and hit the clock with the hand?

Similarly, in the case of promotion, can a player hit the clock with the pawn after it is removed from the board after a promotion.

I also have seen players hold a piece in their hand during play, typically awaiting a promotion (with queen in hand) or just holding a piece?

Are there any official rules that govern hitting the clock with a piece or even holding a non playing piece during play?

Update: I know it is a bit late, but I the ultimate reason for asking relates to classic chess clocks where the buttons are somewhat small and stiff where pressing the buttons multiple times with your hand, especially in blitz games can get quite painful. 
More recent clocks have bigger and softer buttons so it is not really an issue if using one of those.
This is where hitting the button with a piece is much easier on the hand. Does this have any affect on the final answer?
I feel this is legal. I'm using FIDE rules.

This is the rule that describes what happens with a capture:


  3.1.1 If a piece moves to a square occupied by an opponent’s piece the latter is captured and removed from the chessboard as part of the same move.


There's nothing there about what happens to the captured pieces, other than they are removed from the board.

Now, of course somebody will argue that this rule exists:


  6.2.3 A player must press his clock with the same hand with which he made his move. It is forbidden for a player to keep his finger on the clock or to ‘hover’ over it.


And there it says "with the same hand". But you also have to remove the captured piece with that hand, and once you've done that you have to press the clock, and there is no requirement to let go of the piece. I argue that this rule is intended to be used against people who move a piece with one hand and press the clock with the other, not against using the piece that you happen to have in your hand.

Of course, there is an opportunity for bad behaviour, by hiding pieces in your hand so that the opponent doesn't notice he is behind in material (IMO that's that opponent's fault, look at the board not at the removed pieces), or worse, hiding the piece that the opponent wants to promote to. Or by simple distracting the opponent by constant fiddling with pieces in your hands.

But there are already rules against distracting the opponent, there is also the umbrella rule against "bringing the game of chess into disrepute", and when you want to promote but don't immediately spot the piece it is always acceptable to stop the clock, call an arbiter and have him fetch the piece for you. That is enough ammo to use against bad behaviour.