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I just ran The Star of the Mist and ran into some rule issues. The Brigands (Footpad p.147) have a Resolve of 2, but are Craven. The PCs ambushed the Brigand's Camp. One PC tried to Intimidate Foe and failed. During combat they took down two of the Brigands, so I tried to figure out if they would break and run. Can't find any mechanism to check, so I decided they would. Then I tried to figure out how to disengage and flee, but there are no rules for Adversaries, but there are rules for PCs, p.104 Fly, You Fools! I then just rolled some dice and decided they were able to flee.

This also brought into question, what if the Adversary didn't have Craven? There's no way to reduce their Resolve to 0. This only happens if the GM spends their Resolve in combat. Intimidate Foe only makes the Adversary Weary, but doesn't cause them to flee (which used to happen with TOR 1e rules by reduction of Hate).

Any suggestions on how to resolve these issues?

I'm not entirely clear on your concerns, but I'll try to answer and if I get it wrong, correct me.

Creatures with Hate:

They may opt to flee if in a disadvantageous position, but will never yield or surrender, nor give quarter unless forced by circumstances or direct orders.

Creatures with Resolve:

Foes with a Resolve score lack the relentless
motivation that drives the minions of the Dark Lord, and
may surrender when outnumbered, or when casualties
become excessive.

Both on p143.

You just judge for yourself, as LM, when they would break.

It is possible for a player to reduce Hate/Resolve. For example, the Elven Cultural Virtue "Gleam of Wrath" deducts a point of Hate or Resolve upon a successful attack roll, plus one for each Tengwar (p85). There are probably other ways, but that's example I remembered. Reducing them to zero is not the metric for whether they break or not - that is pure LM judgement.

My personal houserule for resolving an enemy trying to flee (assuming the circumstances merit such a decision) would be that I'd tell the player that the creature is about to flee. They can either just let it go, do an attack for a parting shot, or roll Battle - if the latter succeeds, they outmanoeuvre the creature and it fails to escape. You could mirror the Player-Hero version (creature makes an attack roll, and if it succeeds, it escapes), but I prefer to keep the rolls player-facing, if I can.

On the morale of adversary mobs made up of creatures with RESOLVE.

I have so far simply scaled the number of adversaries in the mob from 1 to 10 .
e.g. five foes? each foe counts as 2.

Anytime I want to (as the LM) I look at how many have been killed/incapacitated at the end of a Round of Combat. e.g. if two foes out of five are "down" then if the d12 comes up with any of the numbers 1 to 4 then those still alive will all break and run.

If an Eye comes up they don't check morale again and fight to the finish.
If a Gandalf comes up they don't break & run, they surrender.