Just curious if their effects would trigger upon getting hit by heads on spikes or would they just end up in a dead pile and prevent a player from using them later in the game

is it because a character in hand is not in play and therefore triggers do not apply?

Head's on Spikes: Choose an opponent. Discard 1 card at random from that player's hand. If that card is a character, gain 2 power for your faction and place the discarded character in its owner's dead pile.

I'm no rules expert but the way I see it, the section on Abilities says: "card abilities on characters, locations, and attachments can only be initiated or affect the game from an in play area unless they specifically refer to being used from an out of play area, or require that the card be out of play for the ability to resolve. Head's on Spikes moves the card from out of play area hand to out of play area discard to out of play area dead pile. Thus you can not trigger their interrupts from an out of play area.

Also, the word "Kill" has a definition including "When a character is killed, it leaves play and is placed faceup on top of it's owner's dead pile. It has to be in play/ leave play to be killed.

Finally Davos and Benjin trigger of :When X is killed". Killed is a defined word and Heads on Spikes doesn't say kill, it merely moves the character from the discard pile to the dead pile, hence they are not actually killed. This means no valid trigger.

If I'm wrong, someone please correct me.

You're not wrong.

Mostly, it comes down to the fact that in order to be "killed," a card has to leave play - not simply be placed in the dead pile. (It's worth pointing out, for example, that if you use Davos's or Benjen's Interrupts, they are still "killed," even though they do not end up in the dead pile.)

Since Heads on Spikes doesn't remove anything from play, it doesn't "kill" anything, so it doesn't create the correct triggering condition for "when a character is killed" interrupts or reactions.

they just end up in a dead pile and prevent a player from using them later in the game

That's a pretty apt description of what Heads On Spikes is for, actually.

Bear in mind that only Unique characters (and I suppose unique locations/attachments/events, though there's not currently any effect that would put them there) care about the dead pile. Some nameless mook like a Tumblestone Knight doesn't care if Ser Bumble of Frogpuddle lost his head last week.