Why does this grounding bar have three different kinds of screws?
If you notice, it has 15 small openings and 3 large.  The others are for securing tbe buss to the panel.
Also, you'll need a lug adapter to secure the #4 grounding conductor as per the panels specifications only up to #6 will fit in the three larger openings.


Edit to (2): I believe anything over #4 will need a lug adapter.