These are usually marked by a continuous thick white line on the right-hand side of the road, about a metre or so out from the curb or the parked cars. It is illegal for cars to enter these lanes except to park or to turn into a driveway, or where the continuous white line turns into a dashed line, usually just before an intersection. Also note that many bike lanes are simply too narrow for their intended purposes, and cyclists may have to veer out of them for parked cars, debris on the road, etc. You are unlikely to get pulled over just for this, but it's a useful excuse if a police officer suspects you for something else, and it can cause you to get a small fine. I'm unclear on whether California respects the rules for cars from places like Arizona where front plates aren't mandatory, but you should probably play it safe anyway and not give a police officer any reason to pull you over.
Radar detectors are legal in California.
You must pull over and let them pass, regardless of the state of the traffic or traffic lights, etc. If you are staying here, then technically you must get a California driver's license after ten day's residence. Drivers with valid licenses from other U.S. States and Canada usually need only pass a written road rules test and hand in their old license. Actually getting your license is not that difficult, even with the tests. If you're from another state or province, you only need to register your car with the Californian DMV if you start working here in California, or you get a Californian driver's license.