Say you are using lore of shadows and you cast mystifing miasma. This spell is only a 5+, so if you only have to roll a 1 since the slann is a level 4, could you just use focused rumination and auto cast the spell?
No, the rules for focused rumination state that the disicpline must be used with at least 1 die for casting. You have to have one die in order to get the extra die. And I think that a roll of 1 is always a fail (on a single die).
A "natural" roll of 2 or less is a failure, even if it would cast the spell normally. Even if you roll 2 dice and get double 1's (and getting a total of 6, exceeding the casting value) you still fail. And as Arli has pointed out, Rumination's "free" dice is only added to an existing dice roll.