The "Hide" action is simply the method in which you utilise the "Hiding" rule, both of these are related to the "Unseen Attackers and Targets" rule.
In a previous question you posted, I left an answer which explains these rules more in depth, and to quote a section from there:
"When you take the Hide action, you make a Dexterity (Stealth) check in an attempt to hide, following the rules for hiding. If you succeed, you gain certain benefits, as described in the "Unseen Attackers and Targets" section later in this section."
As you can see, the "Hide" action is simply the method in which you enter hiding, all the rules for the "Hide" action are described in the "Hiding" rule, rather than the "Hide" action itself, the benefits gained from "Hiding" are the benefits gained from successful use of the "Hide" action, which are yet to be explained...
To answer your package of 4 questions:
- If you are considered as hiding per the "Hiding" rule and "Hide" action, you can't be seen unless someone attempts a Wisdom (Perception) check, or their passive Perception exceeds your earlier Stealth check. However, you can also be seen if your DM decides you make an action that considers you to be no longer hiding, like running from one place to another through the visual detection area of vision of a creature.
- Yes, this is what I refer to when I say the DM decides if you are no longer hiding. In some situations if you move during your turn to attack an enemy from a hiding place the DM might rule in your favour that it's a surprise, but if you move into a visible space and end your turn, most DMs would consider you to no longer be hidden.
- Yes, if you hide behind a single tree with nothing around it, it's pretty clear you're behind that tree. While there isn't much on this from what I can find in the Basic Rules document, there is a sort of Common Sense clause surrounding situations like this.
- Yes, again, if the DM decides you are no longer hiding due to the fact you are seen, you are no longer hiding.
Ultimately, with the "Hiding" rule and "Hide" action, it's much like any other part of D&D 5e, the DM has final decision. If you're sitting on a bench in clear light with a creature staring right at you, there's no rule, without being sneaky about it, that would make you hidden from sight.
If you still have confusion surrounding these stealthier of rules, I'd recommend checking out this answer or approach one of the many D&D Discord servers or subreddits to receive one-on-one help as you appear to have more questions as more is explained. Some tutoring on the rule can help with that.
As further edits have come out and comments against what I believe to be helpful answers have emerged, I feel I have to address the following comment:
"I know you, NautArch, SamsyTheUnicorn, Szega, and others have been doing a great job, but I'm very picky and I'm not quite seeing some dots connect - and unfortunately to me they are important dots like "does Hide make you unseen" and "does knowing someones location negate their Hide" :/"
So, "does hide make you unseen", read the "Hide" action and "Hiding" rule: "You can't hide from a creature that can see you clearly", therefore to hide you must be unseen or at least not visible enough the rules would have you stated as unseen, which is decided on by the DM.
Further, "does knowing someones location negate their Hide", "Hide" is not a condition, whether or not you are hidden or more accurately, subject to the "Hiding" rule, is up to the DM. Typically, if you know where someone is, you can use that knowledge for an attack, but whether or not you see someone is subject to various other rules I have already mentioned; particularly in regards to the "Hiding" rule for being unseen, it's up to the DM.