2) *This will be an enclosed step, so the 2x8 will not be notched like
a traditional stringer. *Won't this be strong enough? *I was planning
on slotting each step into the side of the 2x8s, and finishing up with
a traditional 2x12 stringer in the middle.

I don't like that idea. A 2X8 will not work for that anyway. Use the
2X12 and just cut out the desired riser and treads. Don't notch.
Also as someone suggested, because you might be securing the stringers
to the framing below the deck, you might have to add a 3rd tread on
top level with the deck.