Brake light switch and headlamp rewiring?

Honda Dio DLX

My scooter's brake lights are always on and don't need to hold either of the brake levers to use the electric start. Is this going to drain my battery?
If it is, I can re-wire the whole thing and still start the engine without having to hold the brake levers so that the brake lights won't stay ON.
I just want to start the scooter without holding the brake lever.

And is it completely okay to connect the headamp and park light directly to battery?

If lights are always on they will drain the battery, the idea of holding the brake is for your safety.
You could wire the headlights to the battery but these would also kill your battery.
Honda has wired up your bike this way for safety and reliability.

I advise you have it how they intended it to be.