Is there a limit to the amount of function buttons that I can show?
No, you can choose to show as many as you want?
Can I hide the Functions or Columns dropdown?
Yes, you have the ability through in the UI (Dashboard function) or through Dashboard Config to show / hide all the elements in the Home Toolbar (the Toolbar on the left side).
Can I hide or minimise the Dashboard?
Yes, you can do both. To minimise the dashboard click the small arrow in the top left of the first toolbar (and click again to maximise). To hide altogether choose the appropriate option from the column header menu.