Getting ready to run Haunting of Harrowstone, and I have some questions about haunts. First, can you still damage a haunt after it has manifested? I know you can hurt them in the time it takes to appear, but once they show up, can you still do anything?
Second, how does one go about the researching of the destruction of a haunt?
Anyone?
I do believe you are correct. Well, you can do it after they manifest, but only during the surprise round.
After they show up, all you can do is run way.
All haunts have a gimmick, some action that will end them. But, as RAW goes there's no set hint or method of figuring it out. For an obstacle that can't be overcome any other way, you would think they'd set a knowledge DC, and maybe a higher Perception DC that could be made each round as you study the phenomenon.
I strongly suggest you make some such checks up or your players are probably boned.
I really dislike haunts. The only people who by RAW can do anything are clerics because they can channel. Even other classes that can do positive energy are unlikely to be able to accomplish anything, because with a surprise round, what are the odds that you'll be next to it when it tries to manifest?
Some Haunts (Old Ember Maw, and the Piper of Illmarsh, to name a few) continue their actions even after the surprise round. Old Ember Maw continues to spit flame as long as someone or something is in front of it, and the Piper continues his song as long as someone is in his cell block. In those cases, I allowed my party to attempt to harm/disable them each round. It was pretty situational, though; if the haunt has some kind of physical structure, then I allowed casters to use positive energy spells on it (for example, I allowed the Paladin to Lay on Hands and the Oracle to Cure Light Wounds on the walls of Old Ember Maw, but they could not do the same to the Piper since the text for it specifically says that the music is disembodied.)
As far as knowing about the destruction of the haunt, I just gave my players Knowledge Religion checks for it with similar rules for identifying creatures (DC = 10 + Haunt's CR.) Again, though, it was situational what I told them. When the party found the body of Father Charlatan, one player rolled well on Initiative and on his Knowledge Religion check, high enough to have "identified" the haunt before it even activated. In that case, I told him he knew it was some kind of haunt but nothing more at that point. Once the haunt activated and the party realized what was going on (via the Paladin using Detect Evil...see the text for that particular haunt to see how it works, it was pretty detailed) then I told the player who had made his Knowledge Religion check a little more. I usually did not give them the entire description of the haunt out-right, but at least enough to guess as to what to do.
That was the "easy" way out -- letting them make Knowledge checks. You could have them return to the Professor's personal library, or the church if they are in good standing with Father Grimburrow, to actually do research to identify a haunt.
Another thing that my players did a couple of times when they were stumped (or if none of them made their Knowledge roll), was to go ask Vesorianna, in which case I gave them enough to figure out how to disable/destroy the Haunt. I figured she's been around long enough, she probably has an idea of how the spirits in Harrowstone work.
I am absolutely allowing damage whilst haunts are haunting - it's only sensible. If the party breezes through too easily, I may just knock that to half, or else raise the DCs on those saves. Don't think that'll happen, though.
As to research - I'm actually planning to allow Perception and then Know (Religion) or Know (History) - maybe if necessary even Know (Arcane) - to then 'remind' the character of a story they heard years ago. The story will be similar, but not the same. Ember Maw, for example - the PC perhaps remembers the tale of a thief thrown on a bonfire, who came back to haunt the local village, and they had to bury his bones in the cold earth before he would rest in peace. Hopefully the view of the cemetery pond outside will draw the connection.