Slitherine

To center the selected unit on the map - is there a hotkey for this?

By default, Page Up/Page Down cycles to Next/Previous Active Unit; i.e. those that have not been moved yet (or fired, if in range of the enemy). Of course, if the next/previous active unit is near the edge of the map it will not be in focus in the center of the screen but normally it will, given enough space. You can change these hot keys to something else that you prefer in Options, Controls.