Lighting, Light Fixtures, Ceiling and Exhaust Fans - How to install new wall lights in bathroom

I hoping to install two wall mounted lights, one on either side of the mirror, in a bathroom. The bathroom currently has an existing 8 bulb vanity light centered at the top. My questions, is, what is the best way to remove it and add the lights on the sides? Does each light have to have a electical box mounted in the wall behind it? If so, what tupe of box as the base of the new lights are smaller that the standard ceiling boxes I have used. Right now I am pretty sure the existing light just has a wire that comes out of the wall and into it, with no box behind it. Also, do I connect the existing wire (after moving it from the top) to the first light and then add a new wire from that to the other light? Is that up to code?

Thanks for your help!

Yes you need a box behind each light. Find one that is the correct size. They make different size boxes.
Move the wire from the existing location to one of the lights and feed a wire from there to your other new light. The size of wire depends on the circuit breaker. In a bathroom you should have a 20 amp circuit. That means you need #12 wire.