Something came up in our last game session.

Stay Morr's hand is a reaction which requires favour.

Can a priest cast such a reaction without spending the necessary favour, and then gather the necessary favour to power it? If yes, what is the effect of the blessing?

Yes, the priest can cast the reaction even if he does not have the favor, but as the rules state, the blessing won't come into effect until he has gathered the amount of favor needed.

Cheers,

Yepes

So, in this specific case, is the critical wound cancelled?

How about Minor Blessing, does the check get the white die bonus?