So for example in a mall, Can I take pictures of people without their permission? Does that depend on wether they notice I take pictures or not? Also in Cafes and streets...all public places, I am not really sure about this. What are some general rules? What to avoid? I am located in the United States, Kansas!
I am not a lawyer. Seek one out if you want legal advice.
In the United States, photography is permitted by law in public spaces, and also from public spaces of private property.
You can take pictures of people who are in public spaces without any consent unless it is what I would call obviously questionable to a normal person.
You can take pictures of police officers, criminal activities, and basically anything else you can take a picture of from a public space.
In A Mall/Shopping Center
According to Wikipedia:
Photography on private property that is generally open to the public (e.g., a shopping mall) is usually permitted unless explicitly prohibited by posted signs. Even if no such signs are posted, the property owner or agent can ask a person to stop photographing, and if the person refuses to do so, the owner or agent can ask the person to leave the property.