The official Jazz2 palette is available from the included JCS helpfile. Just browse through it until you hit a section with a mini-tutorial (starring our beloved Dean Dodrill). There should be a link there to a palette you can save to your drive and use in e.g. PSP.
For those willing I'll post up a tileset template including the most basic tiles (e.g. destructable blocks, signs) with the standard template. Upon request only.

As for coloring pixels in PSP, select your paintbrush-tool. From the tool options-box, select (if not selected) the most left tab (showing tool icon, in this case a paintbrush). I use these values (I think, doing this from raw memory):
Shape: Round
Size: 1
Hardness:100
Opacity: 100
Step: 1
Density: 100
If necessary, uncheck the build-up option. And if using a pressure sensitive input device (e.g. Wacom tablet) make sure that on the last tab of all pressure sensitive options are deselected.

Have phun tilesetting!