If I have a Giant figure, say Surtur or The Specter and he is on grounded terrain next to elevated terrain and there is an opposing character on the elevated terrain 2 squares away. Can the giant figure target the opposing figure with a close combat or ranged attack that is 2 squares away from the rim of elevated terrain next to the Giant?

In short, yes to both.

Giants are considered to occupy every elevation level above the one their base is (in other words, if a giants is on sqauer of elevation level 2, he occupies also elevation level 3, 4, etc., but not elevation 1). LOF drawed from or to them take into account the elevation taht hinders least said LOF (in other words, if being of elevatiopn 2 is worse LOF-wise than being of elevation 3, the Giant will be considered of elevation 3 for this LOF).
Where does that lead us ?
The opposing character is standing two suqare away from the giant, and another square or elevated terain is between thme. But because LOF to and from Giants are drawed as if the giant was of the least hindering elevation, the giant will draw LOF toward the character as if he was on the same level (or even one level higher).
The GIant Reach ability allows a gioant to make a close combat attack against characters two sqaure away if they can draw a LOF to them (LOF blocked only by walls, elevated terain and blocking terrain). Here the giant can draw that LOF, so he can make both range combat attack and close-combat attack

yeah I figured as much. Dam, why do i keep gettin g screwed on rules by players who dont even know the new rules! i need to print these out or something so little can make a diff, I lost the game bc of these little misunderstandings. thanks Captain Krueger.