Should you die for your ADC?

Early game no. Later on and is carrying or doing good, Then yeah. Cause if the ADC is bad and you die saving him, it sets you back from supporting the real carry of the team.

Yes.

Yes. If they make it out and have the opportunity to come back sooner to farm, definitely.

as a support main and someone who plays alot of tanks... if you die for a carry its worth cuz

1. as a support or tank player/champ you still are useful due to utility and cc
2. if the carry stays alive they still earn gold and experience and that will help the entire team
3. the carry does the damage... so if you make the sacrifice ( not feeding ) chances are your team can win the fight

but with this mindset if im adc in lane and i see my jungler does a bad gank and or support get caught i will blow sums to save them to keep the enemy from picking them off and getting easy kills which puts me behind. i am all about deny deny deny if you deny the kill, the gold the experience you have a chance

only if you're beta

There's no simple answer to this question. Yes, once, definitely. If it was because of a good play the enemy team made and you saved your adc, your team benefits. Do that as often as necessary, but be observant and do your utmost to avoid such a necessity. If it was because you and/or the adc were playing poorly (especially too aggressively), then ask to play safer. If the adc will not play safer, let them die. That is, don't reward or abet game-losing behavior. Later in the game, if your adc is "just" a marksman and another team member is the "carry", it may still be acceptable to die for the marksman but not if your absence jeopardizes the survival of the carry.