Mouse is generally used with HUD and with aiming at the same time. Workaround for this is that screen is filled with buttons which reset mouse position to center of the screen. Webm version of demonstration
Game telling you that if there's no cursor, you should Alt+Tab ↹ game and see if returning to game makes cursor visible.
Casual Mode 2 game telling you controls after shooting segment. Going into that area ends the segment. HUD cursor is disabled so you can't click "Disable lockcursor UI" to get rid of "Lock cursor" buttons.