For Vision, Daylight and Bright Are The Same
For vision and hiding purposes, there are only three levels of light, as you mentioned. Bright, Shadowy, and Darkness.
"Bright" in this case means it's bright enough that there is no hindrance to vision at all. "Shadowy" grants concealment, and Darkness creates effective blindness if you can't mitigate it.
So yes, for these rules, a torch you're holding and the sun are the same thing, within the "bright light" range of the torch (20'). Outside of that range, the torch stops providing bright light. Get some distance on someone with a torch and you move into shadowy illumination against them instead. (If you have different vision modes than they do, you could actually have different conditions to see them then they have to see you, depending on the light.)
example:
If you're holding the torch, you're in bright light and can't Hide without Cover.
If someone else is holding the torch and you're 5' away from them, you're in bright light and can't Hide without Cover.
If someone else is holding the torch and you're 25' away from them, you're in shadowy illumination. That grants you Concealment, and you can Hide.
The same rules apply for any light source, you can use the Vision and Light table for the effective ranges of different light sources.
So what's Sunlight do?
The sun creates both bright light and bright sunlight. The difference is only in the case of monsters or effects that mention something related to that, like an Orc:
Orcs are dazzled in bright sunlight or within the radius of a daylight
spell.
A torch doesn't generate bright sunlight, so in this case it's different.
This Creates Lots of DM Interpretation
As you noticed, this gets confusing pretty fast when Shadowdancers get involved. Just what is "some sort of shadow", and where is it? Ask your DM. It's relative to the light, the position of the light source, the size of the thing casting the shadow, and the rules don't have anything to say on the matter whatsoever.
How big a shadow do you need to use it? Doesn't say. How much shadow is enough shadow to shadow jump? Doesn't say. How long is the shadow being cast by the enemy in front of me? Doesn't say. (This is probably why Pathfinder changed the wording on some of these abilities to be near "dim light" instead, which is more of a known rules thing than "some kind of shadow.")
As a DM dealing with a player who uses these abilities, it can get pretty confusing to try and sort out. It's actually easier in a dungeon with no light of its own, because if some player is carrying a light source, we can map it out on the board pretty easily relative to them and see where the shadowed areas would be (and which direction the player shadows are going, if you want to hide in the shadow of the Wild Shaped Druid).
But in an outside area at 5pm? Where are the shadows in that? It's a lot of work to sort out exactly how it all works, and it's often easier to come up with a simple rule of thumb and apply that rule of thumb consistently.
Hide
The one exception you mentioned is "how dim is dim enough?" In order to use Hide, you need concealment. Shadowy Illumination provides that. So you need to be in Shadowy Illumination, which is going to depend on what the area's light sources are (but most of those have a radius of providing light, and the table in the first link I provided has those distances).
You also need to be not being observed. If they're watching you, even with Shadowy Illumination, you can't use Hide. "Watching you" basically means they can see you at all, because in D&D vision is omnidirectional: characters are looking in every direction on every turn.
That's part of what makes Hide in Plain Sight so good (with HiPS, you can use Hide while being observed).
There are several fundamental planes: the Astral Sea, the Elemental Chaos, the Mortal World, and the World's two echoes: the Feywild (from which the Eladrin came), and the Shadowfell. And then there's Sigil, the city of doors, a plane which doesn't quite fit in anywhere and may not rightly exist inside this particular cosmology at all.
There's also the Far Realm, which exists outside all of that.
Wizards provided a marvellous map of the planes in this excerpt on the planes. It contains a lot more detail of what's in the planes, but you can glaze over that for now and focus in the big bits:
A full understanding of the planes is inseperable from how they came to be. Bear in mind, all history of the default Points of Light setting is (mostly) from the perspective of living mortals, so all the details are fuzzy and there's a couple of versions of everything. That's deliberate and works to your benefit as DM: you have plenty of room to make stuff up and come up with alternatives. The important parts of the history are clear, though, assuming they're not lies.
A Brief History of Life, the Universe and Everything
Citations in this section are from the Manual of the Planes (abbreviated to MOP), the Dungeon Master's Guide (DMG), and The Plane Below (TPB), the sourcebook for detail on the Elemental Chaos. (For further reading there's also The Plane Above for the Astral Sea, and specific sourcebooks like The Shadowfell and Underdark, but I'm not quoting those here.)
The Astral Sea and Elemental Chaos
Once upon a time, there was only the Elemental Chaos and the Astral Sea. Nobody's sure how these came about, because this happened before all mortal or immortal life.[DMG 160] In the former arose the Primordials, the embodiments of Chaos.[DMG 160, MOP 70] In the latter arose the Astral Sea's version of the Primordials: the Gods you probably know well, and the embodiments of Order.[DMG 160]
Birth of the Mortal World and its Echoes
Eventually, the Primordials wanted to create something altogether new. They took some of the infinite stuff of the Elemental Chaos and crafted the elements into a great, spherical world - the Mortal World in its earliest form was born, then still just as hostile and chaotic as the Elemental Chaos itself.[MOP 70] The Primordials further stripped away the brightest parts of the world, and the darkest shadows of the world, and cast them aside. They would eventually recoalesce: the brightest parts gathered together and became the Feywild, and the darkest parts became the Shadowfell.[DMG 161]
Later, the Gods would take notice of this experiment. They visited the Mortal World and stabilised it, separating it into seas and land masses, and sprinkling it with life, making it what we know now.[MOP 70] The Primordials eventually discovered this, found their work of art desecrated with Astral life and stability, and wished to return it to the chaotic thing it was before.[MOP 70] Thus the Dawn War was fought between the Gods and Primordials over the fate of the World.[MOP 70] The Gods won, and the Primordials who survived the conflict were imprisoned or scattered far throughout the Elemental Chaos.[TPB 65]
The Far Realm
The three planes, however infinitely large they are, are only a small bubble in a greater and unknown cosmology. Beyond all we know lies the Far Realms, the origin of many aberrant creatures who are strange and alien and generally seem to want us dead or just make us end up that way anyway.[MOP 30] Please do think of Lovecraft, and think of it as only the least of what the Far Realm may have to offer.
If there's anything that actually knows how the planes came to be, it's probably from the Far Realms, but it's unlikely you'd be able to communicate very effectively with whatever ancient thing witnessed the birth of the cosmology itself.
Sigil
This demiplane serves a role as hosting many secret gateways between the various locations in the 4e cosmology. Elsewhere in a comment on a now-deleted answer, Wesley Obenshain summarised this plane very well (and with more knowledge than I have about it):
Sigil originates completely outside the 4E cosmology. The City of Sigil was a demiplane controlled by the Lady of Pain which itself was located inside a torus on top of the infinitely tall Spire at the center of the plane known as the Outlands which is, in turn, the primary access point to the various aligned plains. Sigil and the Lady of Pain themselves have no confirmed origin.
More info can be found in the Manual of the Planes on page 25.
How are they connected?
Sigil, the City of Doors, is connected to assorted doors everywhere.
The Mortal World, Shadowfell and Feywild are intimately connected. Wander through the brightest, wildest places in the Mortal World and you may find yourself stumbling into the Feywild,[MOP 34] and likewise for the deepest or darkest places.[MOP 50] Connections come and go, and people do get lost there, just as things there may get lost here.
The Mortal World is not as well connected to the Elemental Chaos or Astral Sea, though. One can stumble across connections to the Elemental Chaos in deeply elemental places still,[MOP 64] but connections to the Astral Sea are rare.[MOP 86]
Of course, creatures who know the proper rituals, possess the proper powers, or who know where the breaches between the planes can be found, can easily traverse the realm. There are several of these methods in the Manual of the Planes.
Fan theories
There's a few, but here's two. The nice thing about how D&D 4e's lore is handled is that fan theories can pretty easily be adopted as truth in your campaign's lore.
The Shadowfell and Feywild: our past and future
The Feywild and Shadowfell may represent the past and future of the Mortal World: the former is the World an eternity ago when it was young and teeming with life, while the latter may be the World's distant future, when it is ancient, barren and dying.
The planes are an impurity in the cosmos
It's possible that rather than aberrant creatures from the Far Realm being the intruders, we are. Our small bubble of creation may actually be an impurity and infection in the greater cosmos, and the aberrant creatures are the white blood cells working to cleanse it.
(Both of these I picked up from another of our members, BESW.)
Best Answer
This question is campaign setting specific. Fortunately, thanks to the Spelljammer campaign setting, the answer is actually known for some of the major published prime worlds.
Krynn (Dragonlance) and Toril (Forgotten Realms) are both planets that orbit around their respective suns and spin on their axies as they do so; At night, their suns are in the same places they are during the day, just illuminating the other side of the world.
Oerth (Greyhawk) is unusual in that it is part of a geocentric planetary system; Its sun is actually its third satellite. It's still a planet, though, and it being night still just means the sun's currently illuminating the other side.
That second point actually answers the general case: The Greyhawk campaign setting's geocentric model is specifically called out as a departure from the norm of a system's primary body being a sun that everything else orbits around. It seems clear that the default assumption is that most campaign settings take place on spherical planetary bodies that orbit suns unless explicitly stated otherwise (as it is in the case of your homebrew setting).
Oh, and to clarify something, "a flat surface" is just one of the many meanings of the word "Plane." It can also mean a device for smoothing wood, a kind of heavier-than-air flying machine, or a level of existence or thought. It's that last definition that we're dealing with here, so just because the Prime Material Plane is infinite doesn't mean that any of the surfaces it contains are.