[RPG] Does a natural 20 initiative roll have any special rules

I'm going to answer this question in a system-agnostic manner, as the question posed is one I've had to address a great deal in my own games despite never actually running Numenera specifically. (I tend to run superhero games, so it's quite a regular occurrence that I have to balance combats for a diverse group of character abilities.)

Your first priority is to not get blindsided by this in the middle of a session. So if you don't already do so, I'd recommend screening your pre-written adventures in advance and eyeballing the stats of the enemies for potential problems. You won't always be able to find all of them, but something really basic like the issue presented (the enemies' damage is the same as the players armor), can be caught pretty quickly.

Regardless, whether you're re-balancing the encounter prior to running it or you realize that something's wrong mid-session, ultimately you have to answer a couple of questions in order to know how to proceed.

What purpose should this encounter serve?

Is this supposed to be a major battle, or a speed bump? Not every battle has to be a huge, life-or-death struggle; occasionally, the only real danger from underpowered enemies is to make the players use resources (ammo/energy, spell points, etc.) defeating them. So, the first thing you need to decide is how much the story would or wouldn't be served by letting the encounter be a (relative) cakewalk.

It's a speed bump. How do I handle it without it being boring?

If the conflict isn't supposed to be a major encounter in the story, sometimes it's best to just acknowledge that the enemies are out-classed and let the heroes roll over them. You don't want to do this a lot, because it removes the challenge from the adventures if the only real danger is the Big Bad at the end, but never underestimate the yay-factor of letting the big fighter crack his knuckles and go "Guys, I got this." Players love that. It reminds them how far they've come from the days when a hacked-off kobold with a pointy stick could put the fear of $RELEVANT_DIETY into them.

If you're going to do that, let the encounter be over quickly. As previously suggested, maybe let the bad guys know they're outclassed after a round or two and then break ranks and flee, so that the players don't have to tediously mop up a bunch of no-challenge enemies. Or maybe the fighter can simply cleave them all at once. If they decide to try something like that, let them and move on.

Before I move on, though, I should note that sometimes through no fault of your own, a big-challenge battle becomes a speed bump through player tactics - and generally, after you've got a feel for your group's play style this will become easier to predict. If this happens, decide whether or not you want to let them roll over the battle or dynamically increase the challenge if you feel the encounter is important. (I once had a Sith Lord/Sith Padawan bad guy pair in my Star Wars game where the Padawan proved tougher to beat than her master; the Padawan battle was epic, and the Lord was killed in one stroke by a rogue critical. Dramatically speaking, it worked so I let it slide. It was still a very memorable event for the players.)

Speaking of which...

It should be a challenge. Now what?

Assuming you've decided that you don't want the players to just thrash the baddies and be done with it, now you have to adjust the battle so that the players sweat more. There are a couple ways to do it, whether you spotted the problem beforehand or have to deal with it on the fly. Ideally, though, be ready beforehand.

The first thing to note is that you don't have to run the adventure as-written, in the case of published modules. If, as you found out, the bad guys have daggers and your combat-capable PCs can't be hurt by daggers, then you have to assume that your players will send the most well-armored of the bunch to deal with the threat (see above about player tactics) and equip the bad guys such that they have weapons that will actually hurt the players that will be involved in the battle. (This is where pre-screening the adventure comes in handy; you can decide ahead of time that the enemies are armed with swords instead of daggers. Or that the daggers are magical and do more damage. Or whatever. Either way, you won't be backtracking mid-game to be all like, "Oh; they actually have swords.")

Secondly, assuming you don't want to juggle the stats of the enemies, it's perfectly okay to add more of them, for similar reasons. After all, the module author doesn't know your party. You'll have to make adjustments. (Although if none of the enemies can even damage the players, doubling their number won't help!)

My personal favorite, though, is to have the bad guys fight "above their station" by using dirty tricks or clever tactics. The aforementioned flanking is a good one, as is trying to get around the tanks to get at spell casters once the bad guys know the players have them. Also, (and this depends on the system), non-standard attacks such as grappling, improvised traps, throwing dirt in the player's face, or anything else that a desperately out-classed enemy might do, like ganging up on a single opponent or trying to disarm them so that they can be pinned and slain. This way you're acknowledging that the players are still better than the enemies, but that the enemies are still going to make them pay a dear cost for their victory assuming they decide to go down fighting.

My other personal favorite is to mix different types of enemies together, such that deciding how to engage them becomes part of the strategies that the players must use. Even something as simple as adding a leader to the baddies who can fight a little better gets players trying to decide how to approach the fight; do they commit their big fighters to focusing on the leader while the minions paper-cut them to death (or try to hold their legs, etc. so the leader can behead them?) or do they risk the spellcasters/thieves with the minions to protect the fighters?

What I usually do is to make an enemy or two specifically tailored to the heavy-hitters/tanks in the party and give him minions that would be more appropriate to the rest of them, and maybe a third 'wild card' that can enhance the fight in other ways, like a mage/sniper/healer/whatever.

Anyway, there are a lot of ways to beef up an encounter such that it challenges the players. Generally speaking, though, you want to make sure ahead of time the purpose of the encounter so that you know how to handle it if the situation arises. If it's not important, don't bother. If it is, but you don't want it to be complicated, just tweak the stats/numbers of the bad guys. Or, if you can, simply re-write the encounter and tailor it to the party's makeup. That's the best route, but takes the most work.

No.

You have to choose to Power Attack on your turn as part of your attack action:

On your action, before making attack rolls for a round...

And the AoO rules say...

Attack of Opportunity

You threaten all squares into which you can make a melee attack, even when it is not your action.

Attacks of opportunity are special attacks -- they are not a type of action.

When it is your action (your turn), you can choose to make a Power Attack, before you make your attack rolls. You then get the Power Attack bonus for all melee attacks until the beginning of your next turn. This means you do (and must) apply your Power Attack bonus to an attack of opportunity, but only for an AoO made after the action in which you made a Power Attack and before your next turn.

Since it may not be obvious based on the comments I'm getting, the "on your action" language is almost definitely an accidental hold-over from the 3e rules, as mentioned in KRyan's answer. It is not intended to mean on any action, but specifically on your turn.