I'm not quite sure what you are looking for here, the majority of his outfit is too dark to really shade properly

That is absolutely a good first step! Understanding how basic shapes interact with light is the foundation for more complex shapes.
As a rule, try to figure out cones, cubes, pyramids, and flat objects. After that, more oblique concepts like texture come: drawing floating tubes of water, dirt, etc.
Shading is easily the one you want to learn soonest though, as good shading is what tends to elevate a drawing from a flat drawing to a 3d object with volume, however basic!

In order:
dpixels simply has more knowhow and experience with art and that coalesces into a better version of what you tried to make. An understanding of forms, color harmonies, and their use of outlines  are what set theirs above yours especially. There is no shame in this, some people are going to be better than you, focus more on making your way towards these people as goalposts for your own artistic growth instead.
His colors work better because he used (non-dithering) cel-shading, more contrast in his colors, and he added transitions on the outlines to create better color divides. His reduction in the palette also made the individual colors stand out way more with the addition of that contrast. as a general rule I try to keep at least five steps in saturation or value seperate from the original color to create a visible contrast, but it can be better or worse depending on your light source and intentions with the colors.
Finally, that's subjective entirely. Both can work, so long as the art style of whatever you're designing around is built around that stylistic choice. For example, paper mario games use the thick outlines to highlight how flat the characters are and make them appear more cartoony, while in games like Golden Sun character sprites take a more lineless approach to create a sense of higher graphical fidelity. In this case there's no definitive "right way," it all depends on what you're looking to create.
I do reccomend starting with normal outlines though, I find them helpful and charming in a lot of ways and applying line weight to pixel art is one of the more interesting things you see done with subpixeling concepts.

To add to the above, dithering is a weird one you might want to avoid for now! It's primary use was to circumvent color limitations to create graduated color ramps without actually adding a new color, like in the example I made here:


While it CAN make for an interesting stylistic choice, for example as an emulation of crosshatching methods, try not to let it become your default method for shading! I used it as that for a good while and most of my early work came out looking very gritty and noisy as a result. Try to work with cell shading more often than not, clarity is integral to pixel art!