Your outlines are really good! I think the rook and the knight could be thinner though, personally.

Here are two (really rough!) ideas for giving an idea of 3D shape using shading. If you want to do this, don't just add grey pixels to the edges! Doing that will at best make things look soft and fluffy, and at worst embossed.
First, pick a viewing angle and projection. It's good to be consistent throughout the image.
Instead of just drawing lines inside the piece, you can draw a curve through the whole shape, following the line where the directly-lit area meets the areas that aren't in direct light. Then add some darker shade where even less light will reach. (Under things that jut out on the opposite side, for example.) This is a pretty shabby line TBH (and the perspective is still a bit off), but I didn't want to spend too long on it. I hope you get the idea!
The second piece is an example of how following even a simple rule can get a half-decent shiny effect. Just create a consistently thick line of shine one pixel from the edge. (You can make it thinner for thinner sections of the piece, which helps).
Or try using a reference. I did a quick search for "chess piece" in Google Images and there were lots of examples of pieces in different lighting, or using different drawing styles. It can be fun working out how to get similar effects using large pixels.
Best of luck!