1. How do I make the chrome parts (mirrors, headlamps, door handles) reflect the world?
That's done using a material parameter when you convert the texture for use in Source, specifically
$envmap. You'd best read up on material files in general for this since there's a lot you need to know and still more you're likely to find useful, like how to enable phong shading to add a subtle sheen like the dumptruck.
I personally recommend splitting the UV map for those parts out into a separate (small) texture file, to keep it from looking like crap in Hammer. Hammer disregards envmap masks, which is the only way to define which parts of a single texture are shiny and which ones aren't. For reference, the Land Rover in the swamp pack doesn't do this;
Rexy's vending machine does. I don't know of any other models, official or otherwise, that mix shiny and non-shiny elements. Note that you probably should still use an envmap mask on the shiny parts' material to match the ambient occlusion.
2. What do I do with the windows since there is no interior?
Just black them out. Or, like, brown them out like the Sniper's camper van.
3. How can I make the headlamps look like they're actually casting light? Or should I just make them dark?
Another material parameter,
$selfillum. This one
can just be applied to the entire texture and then filtered out using a mask texture.