What month are you planning your visit? What camera body will you be using?
1. You may be stopped if you're on a sidewalk, but police usually just ask what you're up to. Many times passing motorists will call the police because they think photography looks suspicious, and when called the police are required to respond. They will do what is called a field inquiry, and I've been with foreign photographers when this has happened. Just keep your passport on you, answer their questions honestly and it should be fine. Note: this has only happened to me around 5 times and I've photographed at
LAX more than 100 times so it is rare.
2. I've shot with as long as 1120mm effective length on a 7D+500mm+1.4TC. It depends on the time of day, time of year, and the type of shot you are looking for.
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Photo © Matthew Wallman - Jetwash Images
3. Star out of Hawthorne Airport. They have a webpage with information on aviation photography.
-Matt