To the best of my understanding, from playing the game, there are no stealth elements to the game except for one part.
The enemies usually don't wait in one place guarding or patrolling and "waiting for you", but are attacking you in waves, and everyone knows where you are, even if you are hidden.
A great example, is that there are levels where you can "roam" free at the start, until you steal, fire a weapon or use a vigor (even without hurting any one) and immediately all the cops in the level will come to your location and attack you, even if you were in some room alone, they will attack you.
The only exception is near the end of the game (minor spoiler ahead):
where there is an enemy with a "search light", if you are in the light for a few seconds it will attack, if you are caught for less the the time needed, it'll continue as if it didn't see you. You can run, jump, fire and do whatever you want behind its back as long as you don't get caught in its light.
From my experience, it has no stealth elements at all.
There is one thing which is the detection range of mechanized enemies, turrets, Patriots and Zepplins. They have a detection range and even a detection delay. And there is gear that affects it (probably reduces the detection range). I wouldn't call it a stealth element, because mechanical enemies are seldom alone, and once a patriot or a turret sees you, it'll know where you are and fallow/fire suppression fire, even if you are hidden from sight. This can be counted as a stealth element, but it's a very small one.
Turns out the bodies of knocked-out enemies disappear after a short while like the bodies of enemies that are dead — even though knocked-out isn't really the same thing as dead. Either way, maybe Elizabeth was right.
That said, it's best to keep going anyway. There are far more pressing issues to be taken care of, like
rescuing Sally.
Best Answer
I'll make this as simple as I can.
There is no Prime Comstock and Prime Elizabeth, as there are multiple Elizabeths and Bookers and calling one of them Prime is a bad idea.
Essentially the Elizabeth from Infinite and BaS Ep1 is dead at the start of Episode 2. The Elizabeth that we are playing as sees her other dead self.
The Elizabeth that that we are playing as is from a different timeline where she feels regret for leaving Sally in the vent to die. She came to this timeline to rescue our Sally from the same fate. She looked through all of the tears and found the one instance where she had killed Comstock and died herself.
Yes, all Bookers are dead because the one that went down to Rapture in order to find his daughter is dead. All of the rest were drowned at the end of Infinite.
I'm also adding the definitive video that I've found that explains the entire story. It's a GREAT watch: Here you go