Ye Olde Inn

The rules don't say that monsters get death saves, so someone will say that this part is simple under the NA rules (or any rules)... a monster that gets to 0 body points is dead, remove them from the board (and dispense any rewards in the notes).

But monsters that have healing spells to eventually appear (Frozen Horror the "Soothe" spell). Should monsters only be able to heal on their own turn or get a bonus like the heroes do?

Here we'd get back into the old debate over death saves. Some would say "if you have not used an action on your turn" means that Heroes can ONLY use healing spells if they die on their own turn (not if they are killed on Zargon's turn by a monster). When would a monster ever die on their own turn? Mage of the Mirror (EQP) introduces the Ancient Staff, an artifact that turns the enemy's spell back onto not only the spellcaster but all of the other monsters in the same room!

Granted, having multiple monsters in the same room that have spells is going to be pretty rare (not sure it even was possible prior to Rise of the Dread Moon) even rarest of all that more than one of them would have a healing ability.

I would treat Zargon's "turn" including multiple monsters as "action/movement per character" similar to how a human player could be controlling a hero AND a number of mercenaries. You get an action for each character, not just one action per turn (just as a single human controlling multiple heroes could do a death save for each hero if someone they were all killed at once, which is certainly possible with powerful spells like Firestorm or certain nasty traps).

I'm inclined to let the monster do a death save in those extremely rare cases where he has a healing spell to save himself even if he's killed on the heroes' turn because I take the interpretation that heroes can use a healing spell "off turn" for a death save as a special exception (some who agree with me on this would say the hero forfeits his action on his next turn if he does this, but I don't and so I'd give the monster an action on his next turn as well).

RAW, no they can't, because we aren't told that they can.

That said, I regularly include special things like that to shake things up. For example, since my kids run a total of six heroes I recently reworked Gulthor into a 6 AD, 6 DD, 6 BP monster of a boss (well, I thought he would be) that could attack multiple heroes at the same time and upon getting reduced to 0 BP clutched an amulet at his chest that began glowing red-hot, said "Dread Flame take us all" and then got a second phase where he started at 6 BP again but each BP of damage also reduced his AD and DD by 1. If he had reached a third turn he'd have exploded in a Firestorm dealing 3 BP to everyone in the room, but on the following turn he got put to sleep and he was dead before Zargon got a turn again (so the Dread Flame only took him instead, leaving nothing but ash; my kids loved it).

So as a homebrew option, why not. It is the kind of thing that helps keep players on their toes.

As for that debate, I can't understand how there is one. "If you are a spellcaster with a healing spell, and you have not already performed an action on your turn, you can be healed by casting the spell on yourself." The context (you are given this information in the section about Zargon's turn, which can only come around once all of the heroes have had a turn) is clearly not limited to being reduced to zero on your own turn. The obvious reference would be going back to your most recent turn. This is one of those where I find the text in the rules more than sufficiently clear while I can acknowledge that it could have been clearer (saying "and you have not already performed an action on your most recent turn," for example); to me there is no debate. Thus, there would be no reason to run monsters that way as well.

(I personally find it as more evidence that we are meant to treat all of the hero turns + EWP as being one big turn for the purposes of things like Monk Styles and the one style per turn limit (so no using a style during the Monk's turn if you want to be able to negate damage during Zargon's turn), but in that case I can acknowledge that the wording and context is more ambiguous. For death saves, once you take the context into consideration I don't see how there is any debate.)

It is almost a necessary evolution. With all the expansions we have now, Heroes get surprisingly powerful simply by upgrading their gear.
There are ways to boost the monsters, in particular, using the bonuses that are applicable in the APP. But it is just a first step.
I allow named monsters to use Hero rules for everything. Simple as that. Call it the "Nemesis" affect.