Moving objects with the cursor should move them along their axis of rotation and not just straight up and down.

When an object is selected it moves straight up, down, left and right using the corresponding arrow keys. But usually if an object is rotated, you would like it to move along its axis of rotation. If an object is turned 30 degrees, pushing the up arrow key should move it a little up and to the left (30 degrees), keeping in line with its rotation.

This behavior seems more natural and usable to me than a straight movement. The vertical and horizontal movement could be done by using Alt + arrow keys (as Ctrl and Shift already have other functions associated with them).

Same goes for Shift + arrow keys which now moves the object quite more than just a simple arrow. I think it would be better if this would be changed to Shift + Alt + arrow keys and the normal Shift + arrow keys should go along the rotation axis.