There are actually nine different Flip commands; three for multiple selections (more than one group or loose geometry, etc.), three for groups, and three for components. The three commands that are displayed is dependent on the selection. FWIW, you could just draw a temporary bit of geometry to select with the group or even select a guideline with the group before flipping.
The axis orientation is normally determined when you create the group. Considering where the axes are in that group, I expect you copied a group that was modeled on axis and shortened it to make this wall. then you rotated it into place.
Keep in mind that axis orientation can have an impact on how textures get applied when you edit the groups for that part of the modeling process.
Is this building being constructed from SIPs? It seems to be kind of an odd way to model a building in SketchUp.