Siphon

At the end of this The fallback content to display on prerendering The fallback content to display on prerendering, remove 1 HP from each non-The fallback content to display on prerendering within The fallback content to display on prerendering. Place all HP removed under this unit's chip (may exceed The fallback content to display on prerendering stat).

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Is Siphon considering taking damage?

"Remove 1 HP" is not considered taking damage.

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Does Siphon effect units that are untargetable (e.g. Stealth)?

Untargetable units are still effected. Siphon is not a targeting skill and Stealth just prevents you from being targeted, not from being affected by any skill.

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Will a unit with Siphon remove it's last HP and defeat itself?

Siphon affects each other non-quest unit in range. It's not meant to defeat itself at 1 HP.

Source