Hexproof from blue means that Sporeweb Weaver can't be the target of blue spells your opponents control or abilities your opponents control of blue sources.

Sporeweb Weaver's last ability triggers just once, no matter how many things deal how much damage to it at once (most likely because two or more creatures blocked it).

Sporeweb Weaver's last ability triggers even if the damage causes it to die.

If your life total is brought to 0 or less at the same time that Sporeweb Weaver is dealt damage, you lose the game before the ability goes on the stack.