Here is how it goes down...
.......W
....../
XX/
00X
00X
..A\
......\
.......Z

X = Barrier

OO
OO = Sentinel

A is a character with Stealth, sitting on a bush.

Z is an enemy with a ranged attack. The \'s are his line of sight.
W is an enemy with a ranged attack. The /'s are his line of sight.

Can Z shoot the Sentinel? I know that he can't shoot through the barrier if he was straight off to the right or straight above. I also know that diagonally adjacent blocking terrain are treated as continuous. Therefore, W can not shoot the sentinel.

I may be wrong, but from what I understand, stealth people cannot be shot through. If you have W.....A.D then W can't shoot A because of him having stealth (still sitting on a bush). W can't shoot D either because A is in the way and counts as firing through 'blocking terrain'. Please correct me if I'm wrong on this matter.

Here is the problem for me. You can see Sentinel no matter what. But your line of fire still passes through that square containing the person that blocks fire.

If it was anything besides a Sentinel, then the LOF would be blocked for Z. But because Z is attacking a Sentinel, the LOF ignores standard characters in the LOF. So A is ignored. Because of this, Z does have a LOF on the Sentinel.

Correct.

It isn't because of drawing a LOF through blocking terrain. Characters are never terrain. It is because the character A blocks the LOF. (And it has nothing to do with A's stealth which is not even activated when attempting to draw a LOF from W to D because no LOF is being draw to A, rather it is being drawn through A.)

Standard characters do not block LOF to a Sentinel.

Here is a second question. It really concerns all clix, but I just want to know if it's different because of Sentinel.

XXA
00X
00X

Can A attack the Sentinel through the X blocking terrain. I know diagonal blocking is continuous for LoF purposes, but what about adjacency? Are they still adjacent?

No.

Continuous blocking terrain prevents adjacency. (It's continuous for everything.)