How do the stealth and detection elements work?

Similar to my older questions for BioShock 1 and 2, I would like to know what the stealth elements are, how they work, and how the enemy AI detects the player in BioShock Infinite. This is in case one wants to be extra-sneaky when playing through it.

One of the reasons I asked this question is because BioShock 1 and 2 had stealth elements and even stealth and detection-modifying gene tonics ('gear' in BioShock Infinite) like Wrench Lurker, Natural Camouflage and Security Evasion. Stealth kills can be done on 'unaware' opponents on both of those games. And certain plasmids (Vigor in BioShock Infinite) can make opponents 'unaware' or affect how easily you are detected (e.g. Insect Swarm). I was wondering if BioShock Infinite has similar stealth aspects in its gameplay.

• How does your distance to an enemy, before they get alerted work? Can I sneak near a non-alerted enemy to melee attack or shoot him/it in the face? At what distance will enemies be alerted to my presence?
• Do the sounds you make matter? (from weapon reloading/equipping sounds, gunfire, vigor effects to walking on different types of floor) Will crouch walking lessen sound?
• Does sight or light levels matter? Can I lurk in the shadows? Sneak behind people? Hide behind objects? Being on a different level (a floor up or down)?
• Once you're spotted, is hiding effective? Do enemies alert each other? What if they see a dead body you killed?
• Any enemies with unique behavior when it comes to player detection?
• Is Elizabeth also detected by enemies?
• How does the 'Gear Head' hat gear work? It is described as a gear that will make you "become harder to detect" and "affects automated turrets, zepplins and motorized patriots". How does it make you "harder to detect" by those mentioned enemies?
• Does difficulty matter?

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.

Sight

If there is no scripted 'enemy detecting you' sequence, enemies won't seem to notice you as long as you're not in their view. You can sneak behind non-alerted enemies. It doesn't seem to matter whether you're crouch-walking or running.

However, once you've attacked an enemy, anyone in the nearby vicinity will be alerted to your presence.

In this screenshot, I have been able to sneak behind these enemies, without them noticing me. I have been able to do this in multiple occasions in the game:

Sounds

In one instance of the game, just changing my equipped Vigor immediately alerted the enemies, even though I wasn't moving. They were in the middle of a conversation and the second I change my equipped Vigor, they were immediately alerted. I noticed this at Shanty Town with the first group of police officers I saw.

Elizabeth

Booker should take a few tips from Elizabeth on how to move stealthily. In the screenshot below we see Elizabeth standing nonchalantly in front of and near two enemies. It seems that Elizabeth is not detected by enemies at all.

As far as I know, the only true stealth element is POSSIBLE SPOILER

in Comstock house, you can try to sneak around the Boys of Silence. Although, if you play it right, you can sometimes get to a good vantage point before starting a conflict. for example, getting to a sniper perch of some sorts.