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As Mr Zak and Brenticus pointed out in the comments: Those arrows are always aligned to the global coordinate system and are rendered from the point of view of the viewport camera:

This is likely because the vertices are not aligned. The transform panel shows the median location of all selected vertices; setting it to 0 will move the whole selection as a unit: To align the v …

To transform an environment texture you'll want to manipulate the Generated coordinates: …

You could try is this, however it seems to me you are looking for Custom transform orientations. In your situation: Select the triangle object and enter edit mode (↹ Tab) Select the edge along whic …

This is because the object is rotated 90° around the X axis. So blender is scaling the object around the local Z, then rotating the object so that the local Z is aligned with the global Y. To fix th …

The location of an object is determined by the location of it's Origin. Most likely all your object origins are at 0,0,0, and not in the centers of your objects. To move the origins to your objects, s …

Try using Generated or UV coordinates instead (obviously you need to unwrap it to use UV coordinates). … Cycles procedural textures are 3D, so object coordinates will center the texture around the origin of the object using the material. …

Think in terms of the camera's local coordinates (the local Z is always out the front) …

Otherwise Global coordinates will be used) View The orientation for the View setting is controlled by the angle of the view. … This demonstrates the difference between local coordinates and global coordinates. …