What do I need to change for each arrow to move the object only along one axis, for rotation to rotate only around one axis?

Questions & Answers
1

When I create a new cube, set Position & Rotation to 0 and move the object using one of the arrows attached to the object, two or sometimes all three(x,y,z) parts of position change. Same applies to rotation.

When I add a camera and set P&R to 0 the camera view is tilted around about 30°.

What do I need to change for each arrow to move the object only along one axis, for rotation to rotate only around one axis?

2

This can only happen if your object is a child of other object(s), which have a rotation !=0.

Near the top of the Editor there are two elongated buttons, one can toggle between “Pivot” and “Center” (dealing with position), and the other between “Global” and “Local” (dealing with rotation). Yours is set to Global, change it to Local.

  • Pivot: For every object, place the axis gizmo at its local origin
  • Center: Place the axis gizmo at the (bounding box) center of the object, which is unrelated to its local coordinate system.
  • Global: The axes are oriented along the three world axes
  • Local: The axes are oriented according to the local rotation of the object

If you work a lot with hierarchy and grouped objects, I’d strongly suggest to set it to “Pivot” and “Local”, because then it reflects the real local positions+rotations for every object.