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Fblthp's last ability resolves before the spell that caused it to trigger. It resolves even if that spell is countered.

Fblthp's last ability triggers only if it's on the battlefield when it becomes the target of a spell.

If an effect exiles Fblthp from your library and then lets you cast that card, it's cast from exile, not from your library.

If the spell that targets Fblthp has no other targets, it won't resolve (because it no longer has a legal target after Fblthp has gotten totally lost in your library).

There's normally no way to cast Fblthp from your library or to have it enter the battlefield from your library. You'll have to use other effects to find Fblthp for the bonus card draw.