I can't tell for sure the answer for this question based on the plane description from the DMG. It implies that there's no light in there, but this means it's totally dark or it's like dim-light? Creatures with dark vision can see in there?

It's not dark, it's more muted. Imagine a world with very grey skies and everything feels like you are in a black and white film.

Here is where you can find out more info and se some art:

https://forgottenrealms.fandom.com/wiki/Shadowfell

If you have seen the Sin City movies, I like to think of it like that minus the reds standing out.

It's the Shadowfell not the Darkfell, it looks like you're misreading this 

The Shadowfell, also called the Plane of Shadow, is a dimension of black, gray, and white where most other color has been leached from everything. It is a place of darkness that hates the light, where the sky is a black vault with neither sun nor stars.

"Most color" is not all color.  Think incredibly desaturated color palletes, Sin City is a good reference, as would that asteroid in Thor the Dark World, or really any Grimdark aesthetic.  

The way the Shadowfell is described in the DMG is quite literally "mood lighting."  Mechanical rulings are up to you.  Don't remember what if any guidance DM's are given to Domains of Dread, but I know in Candlekeep Adventure "Book of the Raven" there isn't any mechanical effect on the lighting as far as vision.  However, that adventures does say that usual nocturnal creatures don't need to worry about night/day restrictions because of the sort of "sunless" nature of the world.  

And at night time, or any other dark environment, I rule natural and magical light sources still work as they're mechanically described, but they're not in anyway comforting, but simply illuminate how depressingly dark everything is cast.

I picture the Shadowfell to be like the Upside Down from Stranger Things. Muted, grey/blue toned but still able to see.