To answer the original question and to keep it simple :)
Echoing Longshot, play a healing card pretty much anytime BETWEEN steps.
Explore is a step, which will have generally have an Encounter in it, so as an example, you could heal before your Explore step or after you finish your Explore step (so you can't heal during the Encounter). You could also heal after the give a card step and before the Move step etc.
So is it for all players unless stated otherwise (which makes sense)?
Blessings like "The Midwife", "At the start of your turn, summon and encounter a monster." That would be too "grindy" for all players (thinking about a 6 player game, like we play) and it clearly states "At the start of your turn", so it is an exception?
Similarly, "The Marriage", "At the start of your turn, summon and encounter an ally."
"The Carnival", "All damage is Mental damage that cannot be reduced."
So this one impacts all players?
"The Juggler", "On your check, you may discard a card to reroll a die showing 1." So that is for any player performing a check this turn? (without going into the massive "what means you" debate ;)