Why changing the potentiometer affects the whole circuit?
The brightness of a LED is controlled by the current flowing through it. Current flows through the whole circuit and each element in your circuit gets an equal amount of current, meaning that identical LEDs in series will have an identical brightness, disregarding minor manufacturing process variations.

Now, the current through your complete circuit is determined (in this case) by the total resistance and the voltage of the battery, so when you change your rheostat, the total series resistance changes, and the total current changes.