A quick question:

If you have elevated terrain in a pattern as such, where the X's is grounded terrain, and the U's are elevated terrain:


UUUU
UUUU
XXUU
XXUU


And you have a character at location "C"

UUUU
UUCU
XXUU
XXUU


and another at location "D"

UUUU
UUCU
XXUU
XDUU


is C or D able to draw LOF to one another?

No, its in the November FAQ.

Can hovering characters go onto elevated terrain without climbing up the stairs?

Also, does grounded and hovering characters have to stop on the stairs? If so, do they stop on the first square of stairs or the second square?

Yes. Characters with the wing speed symbol ignore terrain for movement purposes.

Why would they? I am not sure where you are going with this. Do you mean that there is an opposing character in an adjacent square? Please clarify your question.

If all you meant was simply climbing a set of stairs with out any opponents or hindering terrain entering the equation, then no, characters do not have stop when climbing stairs.

Actually, it can. It says in Complete Rules of Play

If an elevated character is on the rim of elevated terrain it may
make ranged attacks targeting grounded characters and be the target of ranged attacks by grounded characters. If the line of fire between a grounded character and an elevated character crosses any elevated square not on the rim of the elevated terrain, the line of fire is blocked.

In Thawmus's scenario, line of fire from the grounded fig to the elevated fig does not cross any elevated terrain not on the rim. Therefore, both can attack each other.

GreatArelius1 is correct. As he said, the answer is in the errata documents. That line you quoted from the rule book has been changed because it with its wording, it allowed some really funky LOF issues to come up (like being able to shoot the entire length of a building, even around corners, as long as only the rim was involved).

From the General Errata document:

Replace the last sentence in the third paragraph under Elevated Terrain, page 26, with: “If the line of fire between a grounded character and an elevated character crosses any elevated square not on the rim of the elevated terrain, or any square on the rim not occupied by the target character, the line of fire is blocked.”

In Thawmus' diagram, LOF would certainly pass through rim squares that are not occupied by the elevated character. As such, LOF is blocked.

Whoops, my bad.

GreatArelius1 is correct, as normalview stated. In fact, C can ONLY see out along the diagonal, as such --

C has LoF to the bolded Xs, and to the targets only on that line.