The laws vary by country, state, and municipality. But usually the laws will somehow encompass the following:
You may generally shoot photos of anything you want which is generally visible and exposed to the public if you are standing on public property, with a few exceptions.
You may NOT shoot photos of anything regarded as a classified or secured area. As an example, the security screening area at the airport is considered such a place (you may NOT shoot a photo which depicts this area.)
There is a list of US top secret areas that cannot be photographed. If the area is not on the short list, then you can take a picture of it.
You may NOT shoot a photo of someone in a place where they have a "reasonable expectation of privacy". For example... you may NOT shoot a photo in a public restroom ... even though it's public property (also... that's just creepy.) Keep in mind that "reasonable expectation of privacy" is up to a jury to decide... if someone is outside in their own backyard, but they've planted shrubbery or erected privacy fences and you're finding a clever way to shoot around them... you're probably going to have a hard time convincing a jury that they weren't trying to create a private space and that you've violated it.
Correct.
You may shoot a photo of something on private property as long as you are standing on public property AND the subject is plainly visible (you don't need to do anything special to get the shot because it was in plain view.)
Correct.
When standing on private property (even private property which is generally accessible to the public such as a shopping mall, a hotel lobby, etc.) you must abide by the rules of the property owner. If there are no rules, then you CAN shoot photos. If they ask you to stop then you must stop. They cannot confiscate your camera (that would be theft) and then can destroy your photos nor can they force you to destroy your photos. But they can escort you from the premises and tell you not to return. If you do return, then you've trespassed and could be charged as such.
Correct, but you still own the rights to any photos that you have taken.
These rules just have to do with whether you're allowed to snap the photo. What you can do with the photo after you snap it is a whole new set of rules.
If you're taking the photos because you plan to engage in commerce with them then there are more rules which may apply. But as long as you're just taking the photos for your own personal enjoyment then generally you can safely take a photo as long as the subject is visible either on public property or on private property where you are not prohibited from shooting.
As long as you do not use the photo for advertising purposes, it could have been taken on public or private property whether trespassing or not.
Paparazzi is a whole different subject. The paparazzi are generally taking photos of famous people. Usually you'd need a model release in order to use those photos and the subjects typically wouldn't grant such a release. But it turns out the 'press' gets an exception to the rule. The press does NOT need a model release to use photos of people. The paparazzi are essentially working for the press (even if they are freelance photographers (and usually they are), their only intended use of the photo is to sell it to the press.) The paparazzi could not sell the photos to, say, a company who wanted to use the celebrity's image as part of their ad campaign, but they CAN sell the photo to a newspaper or magazine who may use it in an article without needing a model release. That's how they get away with do something that any other photographer would NOT be allowed to do.
