Wrong. Once they have total cover, you are no longer able to watch them.
By your gamist interpretation of the rules.
By my simulationist plain english reading of the rules, this is irellevant.
I saw them go into hiding. Ergo they cant take the Hide action (relative to me) while in their box. At no stage are they hidden. I know where they are.
No advantage, not hidden, and (if an elf of halfling) they remain perfectly visible.
Someone has Greater Invisibility on them. You may know, with 100% certainty, exactly where they are, but they still get advantage because you can't see them attack.
Which is a consequence of the invisible condition (or any time your opponent cant see you).
In this case, the Elf behind light obscurement is not hidden (and never was) so he is plainly visible to me. I saw him duck behind his ficus/ behind the rain so he cant hide there. If he cant hide there, he remains visible to me at all times.
He only vanishes
if he can hide. And he cant hide because Im observing him, just like a human cant hide from me by crawling into a box in full view of me.
Same thing with the hypothetical rogue - if they can break LOS or have something that allows them to hide with partial cover or obscurement even while being observed (lightfoot halflings and wood elves, etc), then they can make a stealth check and you can no longer observe them, even if you know with 100% certainty where they are. That grants them advantage as long as they can maintain stealth until their next attack.
Again, I disagree. My interpretation of the rules tells me that you cant hide from a creature that is observing you. So If I watch them go into their hiding spot, they are not hidden (in game terms they cant take the hide action relative to me; or more accurately they can take the hide action it just automatically fails) and accordingly remain visible.
You may disagree on what allows them to make the stealth check, but that's how the rules are written. .
For the billionth time,
the rules are written in a manner that allows for different interpretations (the main ones being yours and mine). This is intentional by the Devs.
If you want a 'break LOS/ mash the hide button' intepretation, you can read the rules that way. If you prefer a common sense interpretation, then you can read the rules that way.
You're entitled to your interpretation. And I'm entitled to mine. There is no 'one true Hiding RAW' despite you claiming it exists.