Mine and thine
In all of these cases, the problem was confusion over the nature of intellectual property.
I’m not going to try to give you a primer on copyright law. I’ll leave that to the lawyers. And I’m not going to get into a philosophical discourse on whether or not copyright protection benefits society. What I’m going to do here is put up some Dangerous Curves signs so you at least slow down enough to avoid skidding over a cliff.
Published versus public domain
“I found it on the Web” means that the material–article or image–is published. Someone owns it, whether or not there is a copyright notice attached to it. It may not be immediately apparent who owns it, because the site where you found it may have stolen it from someone else who stole it from someone else who…. But it isn’t yours, in any case, and you can’t use it without obtaining permission (which is not automatic) and, often, paying a fee.
The exception is when a creator explicitly states that the work is to be considered in the public domain and is free for anyone to use for either noncommercial or commercial purposes. Even then, you should look for restrictions, such as a requirement that you credit the creator.
Typically, the only way material enters the public domain—meaning anyone can use it without paying for the privilege—is by aging into it. Deciding whether something is actually in the public domain may require consultation with an attorney, even if you’re almost sure you’re right.
What about fair use?
The doctrine of fair use says there are certain circumstances when you can use someone else’s work. Unfortunately, the exact rules for fair use are only determined as the result of lawsuits. So you don’t want to claim fair use in any commercial context (meaning in any book you plan to publish and sell) without consulting an attorney, because you cannot afford to be sued.
Dos and don’ts
Do obtain permission to use other people’s work. Do get the permission in writing. Do understand exactly what you have permission to do, what rights you are buying, and what restrictions apply. (A freelance permissions editor can save you a lot of time and worry.)
Do not copy passages you find in books or on the Internet, either verbatim or with minimal text changes, whether you credit them or not, without permission. Do not copy images you find in books or on the Internet, even if they are images of very old paintings and even if you want to apply visual filters to them and incorporate them in a larger work. Do not copy or quote song lyrics—even a single line—ever, in a book or article for publication. Do not quote correspondence you receive from other individuals without their written permission.
If someone else published it, then someone else owns it. If you cannot determine who owns it, you cannot use it. If you are able to determine who owns it, then you have to obtain (and often pay for) permission to use it. And that permission may come with restrictions.
The above paragraph is your get out of jail free card. Print it out. Stick it on your wall. Link to it if you wish. Just don’t republish it as your own. I would not find that amusing.