Thankyou for everyone's replies. They have been very helpful. I have come to the following conclusions, which I will be implementing in my campaign unless someone can convince I am in error?
Core Concepts
• You cannot Hide from a creature that can see you clearly (requires at least 3/4 cover).
I disagree with this on the basis that if I can see 1/4 of your body clearly, then I can see you clearly. I mean, if I see part of a person lurking behind a rock, I'm going to be way more suspicious than if they were in full view.
• Stealth is an Action. When you try to hide, make a Dexterity (Stealth) check.
I dislike this terminology. Hide is an action. Stealth is the skill that can come into play when you try to hide.
• Passive Perception is the DC your Stealth roll must succeed against.
I prefer to think of it as someone's Perception check needing to exceed your Stealth check in order to find you, but the result is the same.
• Search is an Action that allows a creature to make an active Perception skill check.
There's no such thing as an "active" check. You just make a Perception check, or an Investigation check, whatever the DM calls for.
• Only the First attack roll on a creatures turn has Advantage if they are able to successfully hide.
I addressed this up-thread. You don't get advantage directly from being hidden. You get advantage from being unseen. You need to be unseen (at least not seen clearly) in order to hide in the first place, so the two things are related, but being hidden doesn't confer any additional advantage if you were already unseen. Say you're hiding in an area of darkness and make a ranged attack on someone you can see. The attack roll is made with advantage because the target can't see you. The attack also reveals your location. You are no longer hidden, but you are still unseen, so any subsequent attacks you make against the target will be made with advantage as long as the target can't see you.
• If the location a creature is attempting to hide in is obvious, the creature has Advantage on their passive Perception check (DC +5). Example: creature hides behind a tree and doesn’t reappear, ducked around a corner, vanished from sight but didn’t hear you move away, etc. This is also subject to DM fiat. Example: If a creature repeatedly ducks around the same corner and pops out to sneak attack, it can be assumed the target is expecting the tactic and the creature automatically sees the attacker dart out as they are expecting your re-emergence.
IMO (and I believe I'm in somewhat of a minority in thinking this, if not completely alone), most of what you are describing here are examples of being seen clearly and would prohibit hiding. If I see you clearly, and then you try to hide in an obvious place right in front of me, there is no chance whatsoever that your location will become unknown to me. If anyone doubts that being hidden means that your location is unknown, read the unseen attacker rules. An attack from hiding can't reveal your location if it was known in the first place.
• Disadvantage on Perception checks if target is 50 feet or further away.
Sure, why not?
• Dim Light (shadows): Imposes disadvantage on Perception checks.
Not just dim light, but any lightly obscured area imposes disadvantage on Perception checks, but only those that rely on sight. Noticing a hidden creature doesn't rely on sight because you have to not be seen clearly in the first place in order to even attempt to hide. Noticing a creature that's hidden relies on hearing and/or smell, or tremorsense or whatever, things that aren't affected by lightly obscured areas.
• Darkvision: Can see in darkness as if the darkness were dim light. You see in shades of grey.
Again, how you see has nothing to do with finding hidden creatures because you have to not clearly see them before they can hide from you. Sight's been taken out of the equation.