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Never Forget!
I’ll separate the answers:
1. No. There are reasons (8 of them) listed for giving cautions and the “delay” one is written “delaying the restart of play”. Since, in this case, the ball was in play the only caution would be for “Unsporting Behavior” for intentionally handling the ball.
2. Yes. And no. It depends on what the reason for the caution would be. If it would’ve been for what is called “stopping a promising attack” and advantage was applied then it would negate the caution (because then the attack is not technically “stopped”). But, if it was for a “reckless challenge” or some other reason, and then the player committed another cautionable offense then yes the player could be shown both yellows and sent off (and yes this has happened).
Fun advantage situation: If a player commits a sending off offense (say a violent tackle) and the referee applies advantage (which, to be fair, would be very rare), if the player who would be sent off plays the ball or interferes in some way then play is immediately stopped, the player is sent off and the other team gets an indirect free kick.
Thank you for the explanations!