No, with the schematic I gave you, all boards will have the same resistor value.
Yes you can have a centralized plugin area, but it is not necessary: plug next board at the output of the previous one is OK.
The maximum number of LED is limited by the maximum output current of your Arduino.
Under 5V, a LED will sink approx 500µA with 10k resistor. Check Arduino datasheet to see how many LED can be powered by one Arduino output.
Check your LED datasheet, because it may require more current than 500µA (generally a LED require between 2 and 20mA).
In this case, you should reduce the resistor value.
And so, the number of LED you can connect on the output of your Arduino will decrease too …
One solution would be to use 3 pins connectors (0V, +5V and LED signal), and to amplify current with a transistor on your board.