When part (not the whole) of a sentinel's base is on hindering terrain, do you add 1 to his defense against ranged attacks?

No. According to the special Sentinel rules, there's no hindering terrain to him or from him, because of his height.

Another question related to Sentinel. Can Sentinels range attack past a barrier in an outdoor map? Since he is considered a soaring figure he should be able to right?

Nope. On an indoor map, there's no soaring allowed, even though Sentinel is considered to be so. The barrier goes all the way up to the "ceiling" and he can't shoot over it.

Now, shooting THROUGH it is another story.

Whoops! I misread the question! Sorry about that!

On an outdoor map, I think he can, but I'm not sure.

I meant outdoor map not indoor as I am aware that soaring is not allowed in an indoor map. Does that mean it is legal for Sentinel to shoot past a barrier in an outdoor map?

No - Barrier blocks LOS to and from big figs.
It was in the last faq -not the latest one.

Barrier will block LoF from a grounded figure to a Sentinel, however, elevated and soaring figures can still make close combat or ranged attacks on him.

"No - Barrier blocks LOS to and from big figs.
It was in the last faq -not the latest one."

Was it in the FAQ? I checked earlier but it's not there. I'm gonna look again. Thanks for the clarification.

Hindering terrain does affect LoF to and from Sentinels.

Barriers do block LoF unless drawn to/from elevated or soaring figures. And LoF even to/from an elevated figure will be blocked by an elevated Barrier.

Sentinels are allowed on indoor maps, in case anyone wondered.

What if just a part of the base is on hindering terrain? Does it still affect the sentinel's defense?

When LOF is drawn to that square then YES. Normal combat rules apply.

I hate to say this, but this is incorrect. Because of the Sentinel's size and special rules, a Sentinel has LOF drawn to him and from him ignoring figure bases. Normal combat rules apply otherwise so hinderng terrain is taken into effect.

No one can fire over a barrier, no matter what. Even if they are elevated terrain. The barrier block must be destroyed first. He is considered soaring for purposes of movement through terrain, but hovering for purposes of combat.

LOF is drawn to one of the four squares of the Sentinel's base, not the center of the base. So if one square of the base is in hindering terrain, if LOF is drawn to it the hindering terrain is in effect. BUT if LOF is drawn to the square NOT occupied by hindering terrain, there are no penalties.