1. I'm assuming this means a 2x2 base character can have some of their base sitting on elevation 1 and part of their base sitting on elevation 2?

2. Is a great size character on elevation 1 adjacent to a character that is on elevation 2? Would great size character be able to poison character on elevation 2? I know squares on different elevations are normally not adjacent but thought I'd ask.

1. That is correct.
2. Sub for answer...

You're right about the different elevations not being adjacent, it's the key to the answer. Even though the great size character can see/be seen for line of fire, they aren't adjacent because of the elevation change.

If the great size figure was occupying multiple levels of elevation (one and two, for example), they could be adjacent to a square/figure on the same elevation.

Say, however, that the great size character is just on the edge of level 1 and there is an opposing figure on the edge of level 2.. neither figure is adjacent to the other, and either figure could make a ranged attack at the other because of this. The standard figure on elevation 2 would not be able to make a close combat attack to the giant unless it had Leap/Climb. The giant can make a close combat attack because of giant's reach.