Did Jonah die inside the big fish?

Some thought he did to foreshadow Jesus' death and resurrection.

Jonah 2:

1 Jonah prayed to the LORD his God from the belly of the fish, 2 saying,
“I called out to the LORD, out of my distress, and he answered me; out of the belly of Sheol I cried, and you heard my voice.

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Did Jonah die and go to Sheol and pray?

I don't think so. There is a parallel between "the belly of the fish" and "the belly of Sheol". Sheol is a metaphor for the condition inside the belly of the huge fish. It was a near-death experience. Jonah continued to explain the metaphor:

5 The waters closed in over me to take my life; the deep surrounded me; weeds were wrapped about my head

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He was in a terrible place, like Sheol. But there was hope:

7 When my life was fainting away, I remembered the LORD, and my prayer came to you, into your holy temple.

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He didn't die, but he was nearly dead. The experience was like he had died and gone to Sheol. If he had actually died, then prayed, and then got resurrected, that would have been an incredible event in the history of mankind. The Bible would have clearly spelled out the death and resurrection instead of using metaphors.

Matthew 12:

40 For as Jonah was three days and three nights in the belly of the great fish, so the Son of Man will be three days and three nights in the heart of the earth.

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Jesus compared his death with Jonah's experience but the focus above was the duration and location. Jesus died; Jonah didn't.

Water and Fire said:

Sheol is the grave.

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Right. Therefore ...