This was a fun little level, it still has a few flaws though: x1012y1001 there's a missing 'death tile' just under the lowest flame.
If you jump off the right of the castle on x1011y999 you'll wallswim when you reach the next lowest screen.
x992y1003 has a secret passage that leads to a void screen. Also, when I jumped back down the hole after shifting to the' Pinewood Heights' area (x986y1002 etc) and back again, i hit a void instead of going to pinewood heights again.
x1005y1012 has a hole that leads to void screens.
And I really didn't understand the need for the 3rd key and its room (x994y1005)...
There's a void left of where you get double-jump in the maze, reachable once you've (also?) got high jump and/or umbrella. (it's a mite disappointing there's only the four or so screens, and only one trip to be made. Maybe change up the maze once you've got the double-jump there? or put some some actual dessert in this desert? A reason to come back would be good)
It's good that you filled up that area by the purple key, but now there's a new problem: you get wallswims if you climb up from under. Also, the overhang on the screen with the purple key can be gotten over, leading to a wallswim, and a new void or two. Perhaps you could make a loop? Ensure you can't get up that way again after falling in (or double-jump into the wallswim) and have a path up the screens right of the purple key?
Like so, (where K is the key):
<-<-
-K-^
->-|
It might be simpler to just lengthen the overhang and move those cliffs up a tile (or sharply slope the walls under in a few pixels), but I've never been a fan of sealing off when you can expand. (As a player, anyway. Persons actually making the game in question may differ on this point.)
You can get around the overhang on the screen above the blue key, using a technique I have deemed "double-jumping as I close the umbrella I've been gliding with". (It's very interesting being on the other side of that line. As well as navigating the laser lattice from the outside. You could work with that. Just sayin'.)
Bugs: I somehow fell into a void when falling to Pinewood Heights, but that may have been due to me moving around rather frantically. I also noticed a solid block in the tower in that area, which can be hit from below, resulting in a wallswim - granted, it's not that easy, but still very much possible.
A few bits of level design criticism: almost every bit of danger was a huge surprise to me, and resulted in an unpleasant, totally unexpected death. E.g. the little critter that comes out of the earth in the caves, or the spikes in the right part of Pinewood Heights. In a relatively relaxed level such as this one, dangerous areas should feel a bit more dangerous - maybe the music can hint at some challenge, or a few more lethal critters can be added in safer places, so that the player could realize they should be careful in an area. Those spikes could've been added to some part in the beginning of Pinewood Heights, closer to the last savepoint, in order to make the player understand they're dangerous - without sacfiricing a lot of progress.
It would be great to see another level from you. This one felt really good to play!