1) I've found that posting an ad on
www.craigslist.org works quite well. In the same vein, you may want to post ads in your local newspapers. Specify that this is volunteer work if you dont want to waste time.
2) Seems rather tricky. How complex is the scene with the police car? Is it very long? Do you necessitate several different angles? My suggestion is to carefully plan in advance so that when you do shoot this particular scene so no time will be wasted. Options are to either look for a police car in the street and shoot around the area or straight up ask a local police officer if he would mind being in the film provided you are hasty in doing so.
3) I find it is always more interesting to have an original soundtrack to my short films. Even if some songs may seem perfect for the film, having one tailor made by a student or local artist is much more gratifying. Also, it may turn out to be even more fitting to the script. If you decide to use existing songs make sure you aren't using something too cliché or simply overused. I would contact the record label of the coveted artist as they are most likely the ones with the distribution rights. Depending on the label you may get the rights for free. Usually smaller labels ,and coincidentally smaller bands, allow independent filmmakers to utilize copyrighted material for non-commercial releases if permission is asked. If you plan on having a commercial release for your film, or just making money with it in any way, dont be surprised if they charge you.