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).

You can see light at any range

I did some googling, and while it's pretty hard to find specific citations from scientific studies, the places that I've been able to find say that the human eye can see a candle from somewhere between 10 and 30 miles away. The curve of the Earth is about 3 miles away. Thus, any significant light is at least barely visible from any range that you're likely to have line of effect. The houserule that I've used for a while now is that you can see a light source at ten times the distance that you can see a non-lit object without penalty.

That said, the vision rules in every edition of D&D that I've seen are actually reversed. They only work if both the looker and the looked-at are in the same lighting conditions. The vision rules on PHB 183 state:

In a lightly obscured area... creatures have disadvantage on Wisdom(Perception) checks that rely on sight.

A creature in a heavily obscured area effectively suffers from the blinded condition.

Nothing in those rules says that you can't see a creature if that creature is inside darkness and you aren't. This is clearly ridiculous. This weirdly reversed rule has existed since at least 3.0, and shows how little the designers thought about what to do about differing light conditions.

What this means is that you should rely on your intuition more than the rules for what will give penalties based on vision. Since, IRL, lights can be seen from the horizon, you can probably see someone with a torch from at least a few hundred feet, probably out to a mile or so.

As far as being blinded is concerned, my intuition was always that that penalty happened because you couldn't see the ground beneath your feet, or the things that are around you. Thus, I would rule that a character who can see a light hundreds of feet off is still blinded, except for the purposes of making checks or attacks against targets who are lit up.