I have a question about unity : if the hero fail the test and the card is exhausted, what about the part of the card about all heroes treating the hero with unity as if his search cards are as if in all heroes play area ? Since it is not precisely noted that it is active even if exhausted, how do you play it ?

Thanks

Good question as other similar cards have the note like "even if this card is exhausted" - IMHO this is the same case, even if this card doesn't have this note added.

Recently there has been an extended discussion on exhausted items over at BGG.
https://boardgamegeek.com/thread/2155078/exhausting-items-and-implications/

Judging from the (hopefully official) FFG answer that we got on Death Siphon none of the abilities on Unity can be used if the card is exhausted.

I'm with Ispher in that thread... the Vestments of Kellos case is a very strong point against loosing all passive skills after exhausting a card.