#1-Can a grounded character shoot an opposing fig that is on elevated terrain if the grounded character doesn't have the leap/climb ability?

#2-Can hovering characters shoot elevated characters?

First, the standard terminology issue: "Grounded" means "not elevated, not soaring", not "non-flyer" as many seem to use it. So both questions have the same answer as it does not matter if the figure flies or not. Also, Leap/Climb has no effect on ranged attacks, just on movement and sometimes close combat.

Anyway, figures on ground level can make ranged attacks against figures on elevated terrain only when the line of fire only passes through the square of elevated terrain the target is occupying. What this means in practice is that:
1) the target has to be on the edge of the elevated terrain
2) Line of fire cannot pass through another square of elevated terrain, so "arc of fire" is usually only 90 degres, or 180 if the figure occupies the corner of elevated terrain.

Ok, thanks for clarifying that.

What about giants?

Does a giant fig need to be on the edge of elevated terrain to be targeted?

Well, let's see what the rulebook has to say:
I've highlighted the relevant sentences: The latter sentence establishes that a giant figure at ground level may fire at an elevated foe as if the Giant was elevated (and the same principle applies when the Giant targets a soaring figure) or vice versa. The first sentence, however, establishes that a giant occupying elevated terrain is treated like any other character - so a figure at ground level would only be able to draw line of fire to the Giant if the Giant was adjacent to the edge of the elevated terrain.

Thanks again.

1 more question.

If a giant fig is on the edge of elevated terrain and an opposing fig is below, can the giant make a CC attack as long as the enemy fig is within 2 squares or less?

Like so: (x=enemy fig)

X
______
O

Only if the Giant has L/C (since that allows close combat attacks to be made regardless of elevation). From the FAQ:

Q: Is a grounded giant character adjacent to an elevated opposing character for close combat purposes? How about if the opposing character is soaring? What if the giant character is elevated?
A: A grounded giant character is adjacent to an opposing grounded, elevated, or soaring character up to two squares away, and visa versa. An elevated giant character is adjacent to an opposing elevated or soaring character up to two squares away, and visa versa. An elevated giant character is not adjacent to an opposing grounded character.