(1) It's not sucide.The situation is as follows:
a) The paladin resists IN ANY WAY - talking, fighting, anything other than immediate acquiescence - and he dies and the man dies.
b) The paladin does not resist and survives, while the man still dies.
There are NO OTHER OPTIONS.
Q1 - Do you feel that a paladin's oath obligates him to commit suicide in this case?
Q2 - Is the paladin willingly violating his oath?
(2) Yes, the paladin who hands over the NPC clearly is violating his oath to protect those entrusted to his care (I'm assuming the Oath of Devotion in framing it that way. But any paladin who has staked his/her honour on protecting this NPC is going to be in much the same boat.)
(3) Who said There are NO OTHER OPTIONS? Not the rules of 5e, as best I'm aware. How does bad GMing make it the case that the paladin didn't do the wrong thing?
After all, in character the paladin can't know there are no other options - as per @Wiseblood's recent post, the paladin may (and, if faithful, should) believe that there is still a possibility of things turning out well. And should s/he die, well that was also part of the providential plan.