Changing 2005 Prius headlight assembly: The ballast!

I am working on a 2005 Prius driver's side headlight assembly. Replacing the entire assembly with a new one as the assembly was apparently damaged by someone backing into it. Headlight has been out ever since.

The new complete assembly came threadbare, so a couple of things from the old assembly were used along with a new HID bulb, since the old bulb looked burnt out with that white spot. The thing is the ballast... Tried to mount the old ballast, which had lots of that white oxide corrosion on the outside, probably indicated it was a goner, from the former assembly and the aluminum silver cover plug for the headlight bulb does not fit through the slot provided.

What I did was cut the cable and mesh (inside the mesh there is a red cable and a white one), then pass it through the slot and then solder on the wires again. On testing I got a flickering headlight... something which I read shows that the ballast is toast. Getting a new ballast, so my question is:

Is the splice and solder a decent method for this installation? Why is there metal mesh around the cables, what is its function? Does it need to be integral to carry out some function? Is there a way to open the ballast and remove the cables from that side and just plug them in again? I tried to disassemble the aluminum cap on the other end to no avail... Any advice or questions (if my explanation is lame) are welcome.

And finally, why is this such a poor design, that the ballast needs such machinations? thx