To adjust the movement speed of the these keyboard shortcuts, you can either go the preferences and adjust the corresponding slider, or you can turn the mouse wheel while holding the right mouse button in the 3D view.
To avoid imprecise movements when moving objects in two dimensions, you can limit movement to a single axis when using the mouse. By default, objects are moved on the XY plane in the 3D viewport or on the view plane in the 2D viewports. To move objects vertically in the 3D viewport, you have to hold print_key("Alt");. This works either when you start moving the objects and also during a drag. Furthermore, when moving objects on the XY plane in the 3D viewport or on the view plane in the 2D viewports, you can restrict the movement to one axis by holding print_key("Shift");. TrenchBroom will then restrict movement to the axis on which the objects have moved the farthest. So if you are moving objects in the 3D viewport and you want to restrict movement to the X axis, move the objects some distance along the X axis and press print_key("Shift"); to lock all movement to that axis. When you release print_key("Shift");, the restriction is lifted again and the objects will move to the position under the mouse. This applies not only to moving objects, but also moving vertices in the vertex tool and moving clip points in the clip tool. In the clip tool, the axis restriction only works in the 2D viewports however.
Osiris Movement Cfg