What happens if I have a player (with the ball) on my opponents try line and he is hit with a Dangerous Tackle from my opponent?

As normal both players are grounded and a referee roll is made for the Dangerous tackle. A TMO roll must also be made to see if the try has been scored.

If I take out a player with some 'Dangerous Play' can he then decide to 'Hold On' to the ball?

NO. The tackle is assumed to be so unexpected and so ferocious that he is more concerned about the pain then holding on to the ball.

If I am awarded a penalty after the full time siren has sounded, can I still take the penalty?

YES. You may choose to kick at poles if within range, take a scrum down on that spot or opt for Tap Penalty from that spot. NOTE: If you kick for touch the game will end.

My opponent gives away a penalty and is given a yellow/red card. I play advantage and at the end of my turn I decide that I would prefer the advantage to the penalty. Is his player still sent off for his foul play?

YES. At the next dead ball or restart the offending player will be given his yellow/red card.

If my opponent performs 'Dangerous Play' on my player, can my player use a 'Hand-Off' card to negate the tackle?

NO. The 'Hand-Off' card can only be used in your turn as described on the card. The 'Dangerouds Tackle' can only occur during your opponents turn. It is assumed that your player is not expecting such an underhanded tackle and therefor unable to hand it off.