Does Hinata die when she fights pain?

Answer 1

Yes he does

No he doesn't the only reason tsunade was droped from hokage position is because she is unconscious and in a coma therefore at the time Konaha need a Hokage to protect the village then.

Answer 2

When pein uses his huge Shinra tensei to destroy the village

Tsunade gives almost all of her chakra(even chakra she preserve in her seal on her forehead) to her summons Katsuyu to protect all villagers and heal them if possible

so she is completely drained outta chakra and because of it she is in coma

but in recent manga she has woken up from her coma

Answer 3

yes tendo pain killed hinata.

after that naruto went to nagato. argued about something and nagato cried he used the forbidden jutsu to give life who are died by the pain.