So I didn't used to think this was really possible, but I'm feeling more and more recently that this is possible. I know it happens in Strange Dream (though this is more of a cycle thing, I don't know how universal timers work in this game) with the first red flyer just to the left of the start, where when you get there initially and cross the screen without losing too many frames the enemy will fire his projectile only when you get to the left side of the screen (again, this is timing based, not really manipulation, that enemy always fires with a steady rhythm; the manipulation part I refer to is entering the screen at a certain time or dying or whatever to get him in a different part of the cycle), thus saving you potentially dying. I haven't done too much testing about this specifically, or other cycles in Strange Dream or for that matter the game generally, I just know that there's something odd going on with cycles.

Nor have I really done any significant testing (except just noticing it casually, I play this game a lot and notice these things) about manipulation. There's a moment for example in a level I run called Frozen Mountain 2 where you have to get to a certain point on a certain screen, but there's these spikes around which seemingly makes it very random and so, difficult. When I wasn't trying to manipulate the spikes - they seem random and they go in a certain direction when they bounce off the walls so I always just assumed it was random - I'd lose runs because of just getting trapped forever in unfavorable patterns/cycles. (I say "cycle", I don't really think spike behavior is caused by said universal cycles) However recently I've done one thing specifically to a certain spike, and it seems to fairly consistently go the way I want it to. This allows me to get more runs past this point. (It involves turning Juni around in the opposite direction at a relatively small window of the screen, but as I said I haven't done widespread or intensive testing so this is all just theories) Incidentally, it's interesting that when I reach the screen sometimes, the spikes are in one configuration as their starting point, but sometimes they're in another configuration. It could just be that the level maker programmed the level this way.

These are just some examples; I have more. As said I don't have it down to a science, but a lot of enemies that previously seemed random seem now to be affected by position of Juni on screen. It sort of depends on the enemy. Some enemies are always fixed no matter what and others really do seem to be random (like the grey bouncer for example). I would be interested to find out if there's a connection here. On the subject of universal cycles, they're interesting in and of themselves, though it isn't really convenient to use that for enemy manipulation per se because it really depends on the level, I can't think of too many places where it would be useful. I do know though that when you enter a screen for the first time like I mentioned with Strange Dream the enemies that fire at a certain rate for example will always fire their first shot at a specific moment. After that I'm unclear exactly whether it's timing based (my own bias is that it very most likely is) across the entire level. But it's interesting because when you enter a screen for the first time, that's when it "activates". You can wait before that screen forever and then enter it and it will only then start counting down. ie it doesn't seem to activate when the game starts, as some games do when you turn on the console/start the game/whatever.

Yeah you can manipulate the way that enemies move by moving Juni around in certain ways. I've come up with a few strats in The Machine that involve this. Mess around with strats for your games and try and find fast stuff. Like you said some enemies move in fixed ways, so you can't do everything. There are also some situations in which you can't manipulate the enemies. An example of this is guy in The Machine. Around the 1:20 mark

You start too far away from him to manipulate him in an effective way, but if you were to enter from the right you could possibly do a manipulation for him to move.

Like i said, a lot of testing needs to be done with individual enemies in individual rooms. But I'm sure you can come up with a lot of strats in a lot of different places.

I notice with Sky Flower (normal) that if you do a short jump on the first flower on the screen with the 3 red flyers they tend to stay out of your way on the way to double jump

Edit: I mean on to the flower in the first place

The discussion here is interesting and I would love to know more about enemy behavior because there is certainly something to it. I definitely noticed the cycles of enemies even when I played casually many years ago. I think it's most noticeable with the flying enemies that fire projectiles - when you first enter their screen you do not know when they will fire, it seems completely random. But after they fire that first shot, the pattern appears to be set and predictable, even after leaving the screen. So there appears to be a global cycle of sorts, and it also appears that it begins for each enemy when you first encounter it.

Interestingly enough there is a point in The Machine any% normal where you enter a screen with an enemy twice. The ninja enemy appears to be very RNG based, both in terms of when they throw stars and the trajectory of it. The first ninja you encounter in the blue area, you enter that screen briefly on your way to it which would start this enemy's cycle. You then re-enter that screen shortly after and in my runs, I just run straight past this ninja and I cannot remember being hit by him even once, even though I know full well that he is very capable of hitting you in that position.

Later in the blue area you encounter more ninjas, the ones that are climbing walls, and the screens that they are on you only visit once. These ninjas are a different story, their pattern to me appears unpredictable and I have lost many runs to them. I'm not saying there is definitely a connection between the ninja whos screen you visit twice never killing you and the ones you see only once that do, but it illustrates how knowledge of these cycles do have a direct impact on speedruns.

Another enemy of interest is the black creature that climbs walls and fires three projectiles. There is one in the green area in The Machine, right before you enter the ghost area. Now in any% you just pass this enemy once and I find I can always do the same movement to get past. However in 100% you need to pass him twice and it is a cause of concern to me as the second time the enemy will already have been activated and it can be tricky to get past should the behavior be erratic. I think this enemy moves towards the player but it appears its firing rate isn't set, though I could be wrong. I intend to do some 100% runs shortly and I will definitely be monitoring this, and other enemies you encounter more than once in the run.