Is card laid a card played?

Pretty much - card laid is play made.

Unless for some reason you have some priory arranged 'house rules' that is the way a regulation card game is plaid.

Same as chess, draughts (checkers) etc., in my opinion.

Once contact has been broken with the card or piece, the player's turn is complete, leaving the next player in line free to take their turn.

Yes.

In most serious chess, one you initiate contact with a piece, you are locked into moving that piece as long as it is legal. If you are playing in a tournament there is a phrase that you must say in order to adjust the pieces on the board (i.e. when they aren't aligned correctly in the square).

To avoid being committed to making a move with the piece you are touching you say "j’adoube". This is French which loosely translated means "Oh **** what was I thinking if I move that piece I am lost."