Looks like a fun project! I especially like that control box.
For your servo questions:
Servo angle = stick angle. The servo will move proportionally to the stick. Move the stick to 40% and the servo will move as quickly as it can until it reaches the 40% position and stop. It does not self center unless the stick self centers. If the servo is connected to a channel controlled by a 3 position switch instead of a stick, the servo will move to the 0% position with the switch down, 50% position with the switch in the middle and 100% position with the switch up (The exact positions can usually be adjusted in the transmitter setup with trim, dual rate, mixes and End Point Adjustment).
Bonus technical answer:
Internally, a servo is a motor, ESC and a feedback potentiometer connected to the output gear. The feedback pot works in the opposite direction of the signal from the receiver. If you open the servo and mechanically disconnect the pot from the gear, you can actually control the speed of the motor either with the stick or by adjusting the pot. If you use glue on the pot or replace it with fixed resistors it will work exactly like an ESC and motor. When the pot feedback and stick signal cancel each other out the servo motor stops.
In other words: If stick signal is lower than pot signal then spin motor left. If stick signal is higher than pot signal then spin motor right. If signals match then stop.
Because of this a hacked servo can be used as a motor/ESC combo or a PWM dimmer for lights.
To control lights from a receiver channel you'll need a control board of some kind. This can be a hacked servo, an Arduino, an RC light kit like
this or an RC switch like
this. Frizzen has a great servo light controller hacking tutorial
here in the electronics section.
I hope this helped, but I'm not always good at explanations outside of my own head, so feel free to ask more