CandyFace
If the color palette is based on the first image as you say, then using "Import from image" located in the color tab should give you the exact same color palette, though i am not sure about the order.
Shared Palettes between files
new_name
When having multiple files open, the palettes are also multiple. I encountered that as a problem cause I wanted use the same colors I had on the first file for the second one. For me to accomplish that I had to use the color picker one the first file and set the colors I had picked one by one to the palette of the second file, tried to save and it prompt me up with an error. Sadly I sent the report as anonymous already and I didn't copy the error log.
From my perspective I'll be wanting to perform this task several times through my projects and believe Shared Palettes between files should be added as one of the features for PyxelEdit.
*Don't take this as a demand but as a suggestion (;
Thanks in advance