1a) No (at least not that I know of)
1b) No, other than switching manualy between researched techs every turn
2) There is a "Manage" button at the top of the fleet control box (or whatever the official name of that is
) in the lower left corner whenever two or more fleets are in the same hex.
3) You see damage of ships in the fleet control box only by hovering over the ship with the mouse (very annoying, something like a life bar would be much better).
4) No.