Does a creature dying to 0 toughness use the stack?

So here's my scenario

On my board, I have [[Deepfathom Echo]], [[Reyhan, Last of the Abzan]], and a 1/1 bird token.

I go to combat, and make deepfathom echo a copy of Reyhan. It explores and I dont hit a land. Deepfathom echo is now a legendary Reyhan last of the abzan with 0 toughness. Can I

a) sacrifice reyhan to the legend rule and put 6 counters onto deepfathom, allowing it to survive

b) sacrifice reyhan to the legend rule, put botg reyhan's and deepfathom's triggers to add counters to the bird onto the stack, then lose both of them

c) instantly lose deepfathom the picosecond its toughness hits 0 without even using the stack, but still get a legend rule trigger and have to sacrifice reyhan and move just 3 counters, for only its own trigger and not deepfathom's, to the bird

d) lose deepfathom the moment it hits 0 toughness, but either it dies before the legend rule can trigger, or, trigger the legend rule but be able to just sac deepfathom echo to satisfy it, leaving me with reyhan and a bird?