Without a lot of detailed info on the bike, I doubt that anyone can give you a simple answer like "go buy this battery and plug it in".

In principle, you should be able to build a battery pack of the appropriate voltage and connect it. It looks like it has a fairly standard automotive connector on the bike, so you could buy a mating connector from an auto supply store. I get the feeling that you may not have the technical skills for all of these activities, though.

It might be easier to just remove the lights and install new ones.
As for the brakes... I'm not familiar with brakes that need electric power. Is that just to activate a brake light, or is it more complicated?

Steve in Peoria