Do blocking terrain and barriers work the same in Outdoor Maps? Do they block line of fire when you're an elevated figure shooting over a barrier? Or can you even shoot over a barrier/blocking terrain on elevated?

If you and your target are on say elevation 2, and blocking terrain is on elevation 1, then yes you can.

If you are on el2, and your target is on 1 along with blocking terrain, then no.

So they need to be adjacent to blocking/barrier to have their LoF blocked from e2 shooting at e1?

No, if blocking terrain exist on the same elevation (no matter where it is) as one of the 2 characters and line of fire draws through it, then line of fire is blocked.