New to scooter repair/headlight & idle question

[dmr3073]

I repair our motorcycles but am new to repairing scooters. My son has a 2008 50cc Eagle scooter GY6. Ive replaced starter, carb, fuel lines, fuel filter and valve head. And spark plug. Ive got a couple questions that may sound stupid by i honestly am not sure about because our big bikes are differeant and do not do this...lol
On the headlight: this scooter has 2 front lights that are on all the time. The middle light(headlight)only turns on when you push the high beam on. Is that normal. Or is the headlight bulb need replacing? Because if turn high beam off the headlight is off and just the 2 small lights stay on. I know crazy question. Sorry.
Also is there a way to adjust the headlight, since to be higher then should be, but that could be normal too.
Rear brake:
Our bikes do not do this either so need to be sure if this is normal with scooters or not. Ok, ok when were adjusting the idle speed on the carb (new) we noticed with scoot on centerstand if you press the rear brake(left side) (yes this one you have to press brake to start bike)- anyways when you press the brake while running it idles fast but you release brake and it idles down. Is this norm or why would this be doing this.

This scoot was in rough shape when he got it and just trying to help get it going good. Thank you for you time, help, and patience.