(1)
Most 3D applications use the coordinate system that has been chosen by OpenGL. This is x:left, y:up, z:back. Most Newton examples are OpenGL-based, and so the examples use this coordinate system too. Gravity would be (0,-G,0) in this coordinate system.
Panda3D developers have has chosen x:left, y:forward, z:up as it’s default coordinate system.
By the way: this is where the terms “z-buffer” and “z-buffer-fighting” come from. In OpenGL the z coordinate is how “deep inside” a window (forward) the objects are.
(2)
If it comes to fundamental physics then the choice of coordinate system is not important. Physical laws are the same in every coordinate system, and so every coordinate system will work. Left-handed or right-handed doesn’t matter too.
Problems arise only when software makes assumptions on what coordinate system will be used.
Panda3D assumptions: The default camera controls come to my mind (drive and trackball), both are assuming y is up. But of course you could write your own camera controls…
Newton assumptions: A.F.A.I.K Newton does have only two assumptions on coordinate systems: First, vehicle tired can choose their pin free, but vehicle bodies have to ab aligned in such a way that the “nose” of the care is the positive x-axis. You might want to read this thread on the Newton forum: “Vehicle Joint Bug w/world Z Up and Tire pin along X axis?”. Second, ragdoll bones. There is a mismatch between Panda3D and Newton about which coordinate axis is from bone end to bone tip. So far I have no workaround.
This means you can choose whatever coordinate system you like for Newton. Car meshes have to be rotated so their nose points towards +x. Ragdolls are a problem still to be solved. The Panda3D default coordinate system is a good choice.
(3)
Newton transform matrices do not support scale and shear! So if you use scaled models and apply the matrix computed by Newton, then scale will be reset to (1,1,1).
(4)
For PandaNewton I have been using the same coordinate system in Panda3D and Newton. So conversion of vectors and matrices is 1:1.
If you set gravity to (0,-G,0) and your box moves to the backwards (out of the screen) then everything is fine. Since Panda3D prefers z-up I suggest setting gravity to (0,0,-G), like you did already.
Next I suggest you check if rotations are working right. For example by creating a box and changing heading/pitch/roll, then apply np.getMat( ) to the Newton body, and back again.
I hope this has been helpful 
enn0x
