You can filter your selection. Have a look at the 'Utility Toolbar' which is situated right below the main Menu Bar. In this dropdown list you can select between: All Assembly Part Workplane Face Edge 3D Edge 2D Annotation Docuplane Pick 'part' to limit you selection to parts only.
Also ..... If you place your cursor over a vertex belonging to the part, then select, - the part is selected not the face. a vertex would be a corner - can't be done this way on a cylinder or sphere though!
spheres and cylinders do have vertices, but to know where they are you must turn on vertices in your viewport. Right-click in your viewport (that's the blue background area where your workplane and models appear) and select Show Settings. In the 3D Geometry tab of the Show Settings you can turn on vertices. Also play with the other toggle switches in here to see the effect. Also you can turn on the Show toolbar by going to View>Toolbars>Show. On this toolbar, you can toggle on/off vertices as well plus many other options. Just hover over each toolbar icon to get the tooltip. Try it, you'll like it.
The focus, what will be selected, is always ""Parts"", if you first acivate a parts-command from the parts&assembly menu like copy, position, ... In this case the system expects a part (or assembly) and it is not necessary to switch the focus. If you first select an element, the system does not know, which command you will use next. So you have all the possibilities to select points, edges, faces and parts.