When Inspiring Presence triggers, you aren't playing a heal card. Talented Healer needs you to play a card.
Inspiring Presence is a card, Dwedit. A card you play. That heals. This feels like a bug if it's true (haven't checked).
It works correctly, somehow. Note that Talented Healer triggers on successful play of a Heal card, which I guess only means cards that have the actual keyword Heal in their description. Inspiring Presence, on the other hand, is a card that heal but doesn't have the keyword.
Yes, it does. It's not in the card name, but it's there (and capitalized) in the rule text, just like the vampire attacks. I suspect it may be because Presence isn't targeted.
It states heal in the card description but for whatever reason, the heal is not underlined. This is either a bug or a design decision, but I think that tweaking this to proc talented healer would be a good way to work at some way of balancing priests and make talented healer worth using.
In the current meta, I don't believe talented healer is worth using for priests due to the token cost. If it had more synergy with cards that I believe are bugged [inspiring presence] then it may change in my mind.