1 Ship yard per planet. This was added because someone (Spartanius) created a ton of shipyards at their homeworld so they could create a massive amount of cruisers to attack everyone. Shipyards are the only orbital that is governed by that rule. Even though you can build multiple things like Science Stations, and Refineries their bonuses do not stack. The other issue we encountered was they hit their ship limits and were unable to build a ship yard at any other planet. So now shipyards do not count to your object total, hence why the restriction was put in as well.
The only orbital that has any benefit having more than one is the Missile Array, Beam Array, and Mine fields. This is because they are basically orbital combat ships.
5) We will have the player details in the next client that show your details. The standings will be implemented in the very near future.