Chess Clock

Dear chess players,

I know the general rules of chess, such as the fifty-move rule, and also the details about the three times repeated position-rule, but there is one thing which I wonder.

In all chess rule topics or books it says "you must handle the clock and your pieces with the same hand" but I wonder: may you take a captured pawn with your other hand? I thought I saw someone doing that in a video on Youtube, but of course, that doesn't exactly mean it is legal... (Youtube and reliability, nah..)

And if you castle, must you do that with the same hand or may you move the rook with the hand which you normally don't use?

If someone ever barked that rule I would use both hands to move my piece.