What should the Roll of each bone be? I was about to animate a humanoid character after rigging it but encountered an issue when copy and pasting flipped pose in Pose View. When I paste the flipped pose the leg and arm bones basically are inverted(in painful ways). I read up online and basically found that this is due to the way my bones are rolled. I tried fixing it, but having no luck figuring out which way the bones would be rolled. In Edit mode the model looks okay, but once I switch to Pose mode the legs become rotated.

Which way should the axis of each bone be pointing(x, y, z)?
There aren't any rules for particular roll for particular bones.  For bones that rotate in only a single axis, fingers and such, I tend to make that the X axis simply because it makes it easy to set the roll from a cursor (select tail of bone and head of parent, snap cursor to selection, recalculate roll->cursor.)

A good way to build rigs to get easily mirrored poses is to build only one half of them and then use armature edit mode's "symmetrize" tool to create the other half.  This will provide appropriate rolls.

Another way to fix rolls is to turn on X-mirror in tool options and set the roll for one side's bones individually.  Blender recognizes bone symmetry on the basis of name, not roll, so x-mirror will apply roll changes appropriately even to bones that aren't fully mirrored (unmirrored roll.)