Spigot and spicket are just alternate spellings for the same thing. Both are attested in the Concise Scots with "spicket" being the primary spelling listed and spigot being an alternative.

I just know the saying as "Lang May Yer Lum Reek" and it is just "long may your chimney smoke". Just means I hope you live a long life.

Reek does just mean smoke as it is meant in said saying - but it can also be more specifically an unpleasant, acrid, smoke-stained smell.