This issue sometimes keep me awake at night. Not really. But, I am paranoid that I will do this, if I already have not.
There’s a saying that nothing has be unthought of. So, if thought of a so-called original thought, how can I find out if this thought has already have been printed, in a book or online?
It is only plagarism if you copy without attribution. If you independently come up with the same thought, it’s not plagarism even if the thougths were published before. This doesn’t mean you’ll necessarily be believed of course.
The wholesale theft of ideas is called art and is the foundation of our human society. The wholesale theft of verbatim text is called plagarism and is the foundation of a really short college term.
More seriously, it is impossible to know where all your ideas come from. You half-hear a song about swimming on the radio and you get a great notion to jump in the river. Well, maybe not, but any reasonably good diet of media will expose your mind to more than you can hope to remember consciously. Ideas pass like magnets in the night, attracting and repelling and spawning new ideas out of shared fields.
“Original thought is like original sin: It happened a long time ago to people you you could not have possibly met.” - Fran Lebowitz
Expressing an idea that’s been expressed before is technically plagiarism, but I doubt you would get in trouble for it.
The rules and norms of plagiarism vary from place to place. Most educational institutions set up rules to prohibit deliberate plagiarism. As far as I know, the rules pertain mostly to writing, but some may also pertain to ideas themselves. The latter is particularly true if you are presenting original research for something like a thesis or dissertation.
I can’t believe that someone would unintentionally plagiarize an idea in a dissertation. By the time you get to writing, your advisor, fellow students, and professors should be very familiar with your work. Trying to push someone else’s ideas as your own with experts looking over your shoulder is really hard. Of course, you could have an idiot for an advisor.
As an additional guard against plagiarism, you are expected to document scholarly works with citations and bibliographies. By definition, a scholarly work that was lacking in these, either in amount or in style, would raise questions of plagiarism.
Remember also that plagiarism sometimes doesn’t count. To some extent, you can patent an invention that someone else made, as long as that person hasn’t yet patented it and makes no attempt to claim it afterwards. For example, if you see someone else’s invention, then that person dies, and you patent the invention, you’ve done nothing wrong.
At least, that is, unless his heirs come after you!
Sometimes scientists unintentionally plagiarize someone else’s work. Darwin published his theories of evolution after reading those of Wallace. In that case, though, Darwin’s work was much more thorough, and he had the prestige and social standing to carry forward the ideas. Even so, he asked Wallace for permission. Wallace graciously agreed, and Darwin credited him. A great story.
Then there’s Newton and Leibniz and the calculus. Newton came up with the idea first, but didn’t publish for nearly 20 years. When Leibniz independently developed his ideas, Newton cried foul. We see no evidence that Leibniz stole anything. Newton was, besides being one of the great scientific thinkers of all time, a whacko. 
As I told some concerned students in a creative writing class, you may have what you believe to be an original idea for a story. You cannot always know if someone else, somewhere in the world, has had this very same thought or not. However, the two of you can’t sue each other over a similar thought.
If you want to talk copyright law, it’s my understanding that you can’t copyright concepts but only the expression of execution thereof.
Plagiarism occurs when someone (usually deliberately) reproduces passages, chunks, or the whole of another person's text and presents it as if it were their own creation. Certainly you can have the same or similar ideas as the writer of the original passage. Just don't borrow it without giving credit to the source.Not in the way I understand it, or in the way most people understand it. In fact, this makes all human works plagarism to within a fairly stringent margin of error.
I understand a good deal of patents are improvements on an existing patented invention. I also don’t think most people are thinking of patented inventions when the word ‘plagarism’ comes up.
Anyone can sue anyone for anything. Patent trolls are everywhere. It’s the nature of the system.
Good ones intentionally ‘plagarize’, especially under your definition of the term. According to that whacko Newton, “If I have seen farther it is because I have stood on the shoulders of giants.”
It’s something I’ve got to watch out for as a published writer and researcher- generally there are enough ways of re-writing a given concept so it does qualify as your own work, but every once in a while you come across something that so perfectly encapsulates the point you’re trying to make that you’ve got no choice but to quote it in its entirety and attribute it to the appropriate person.
As the saying goes:
“Plagiarism is stealing from one source. Research is stealing from many sources.” 
I always understood that you cannot copyright ideas, only their expression, but it is clear that this is no longer the case. Otherwise we would not have had those absurd lawsuits over “The wind done gone” (telling the “Gone with the wind” story from the point of view of a black slave and over Harry Potter. (I have forgotten what the allegation was, but it was only about a word, not the expression of anything. I think the word was “muggle”.) These suits should have dismissed immediately with prejudice and legal fees assessed. Instead they wasted loads of time and money. I am just as incensed over the RSA encryption patent. What was patented was not the program, which would have been reasonable, but the whole idea, which was based on a theorem proved by Euler 250 years ago.
At least one computer scientist has suggested using some ideas of mine (and published) as a way of formalizing parallel processing. I say, “More power to him” and I don’t expect to get royalties.
Incidentally, I don’t accept the statement that there are no new ideas. I’ve had several. Tim Berners-Lee certainly had one big new idea (the web) and there are many other examples. The first person who thought of putting many transistors on a single chip had a wonderful idea.
You are confused. Expression can also include characters doing certain things in a certain way. Those go from beyond mere ideas to copying the particular expression of the idea. Considering how little you know about the second case it seems bizarre from you jumping to the idea that it was completely without merit. I remember that case, and I think it had some merit, as it was a lot more than just a word, but a number of important words and similarities.
If you completely rewrote Star Wars with all your own writing that in no case overlapped the specific writing in the movie, script or book adaptations, you would still be guilty of copyright violation. If you didn’t keep the plot and characters exactly the same but changed it a little, that would still be a copyright violation. There is no exact line on how many different things have to be changed before it is no longer a violation. That’s why cases like the ones you mentioned need to be looked at.
Hypertext was ‘in the air’ at the time. Research Project Xanadu, the Gopher protocol, and the paper “As We May Think” by Vannevar Bush. (That’s just off the top of my head. Google has tons of info on all three of those topics, so I don’t really need to provide links here.)