I would like to evenly space these objects, i.e. having the same distance on the left and on the right side of each object. How can this be accomplished?
Use the Align and Distribute panel.
Do the shapes first. Select them and Align: Centre on horizontal axis, then Distribute: Make horizontal gaps between objects equal.
Group the shapes.
Select the black bar and the group, then do Align: Centre on horizontal axis, and Align: Centre on vertical axis.
You need to use the align and distribute dialog.
In order to get equal spacing between sides and between objects, you probably need 5 objects: 2 vertical lines with 0 stroke width on the sides of the black rectangle, plus your 3 icons.
Select the 5 objects, and in the Align and distribute dialog select the option for equal horizontal spacing.