There is an added portion to the Pulse Wave ability in the newest player's guide:

"Pulse Wave does not ignore the effects of terrain."

Does that mean that Pulse Wave does not ignore Stealth, which is generated by an effect of terrain (hindering)?

That should mean that figures would still recieve a +1 DV for Hindering Terrain.

No, it means that the Space map wil still halve a Pulse Wave's range.

What about dairoka's statement. Do figures in hindering terrain get +1 to their defenses now when hit by Pulse Wave?

And, on a more general note, if the only character in range is a stealthed character, can I use Pulse Wave at all?

That hasn't changed. The hindering terrain modifier still applies.
Assuming it is an opposing character, yes.

Yes, you can hit someone in Stealth because Pulse Wave ignores all powers and they do get their +1 DV hindering bonus. FYI this has always been the case so whoever told you otherwise has been cheating.

The rule is making clear that while PW ignores all powers until the action is resolved, it does not ignore the defensive bonuses and blocking effects of terrain.

Since this is an topic about pulse wave. Would a barrier block pulse wave?

Yes. It is blocking terrain.