These are great! I'd buy a(nother) chess set if this was a real. Really well thought out. 
It is okay to have a background for pieces, even if it is just a solid color. Many users have different themes which leads to different background colors, so including his own background gives the artist the most control over how his piece will be seen.
>The white rook
Thank you! It was a vital mistake. Fixed now ;D
They look like they're made of milk and white chocolate <3 Whatever piece you capture, you get to eat!
The white rook (panda) piece has a stray-looking dark pixel near its arm. It looks like maybe you made a mistake when recolouring the black rook?
I think it might be better to leave the background transparent in this case. The green looks great with the warm browns, but since these are just sprites and don't form a scene, it doesn't really contribute much, and in such cases the PJ rules ask for transparent backgrounds I think.
Nice