(But I wonder, if you come up with an invention but don't tell anybody, isn't that a natural property right? I mean, to say that you don't' have a right to it, would be to say that others have the right to forcibly take it from you, wouldn't it?)
Irrelevant. If you haven't told anybody, they have to violate your rights to your property (stealing the plans of the invention) or to your liberty (coercing you in some way to tell them your plans) to obtain your invention.
The whole point of copyright and patents¹ is not to protect your right to the invention, but to give you the right to prevent others from using their legally obtained copies of your invention as they see fit.
Yes. In the absence of copyright/patent/trademark, everyone can use every bit of knowledge they come across.
The "natural right" is the right to use information. Copyrights, patents, and trademark are constitutional limitations of this natural right, hoping to encourage more creation and sharing of knowledge to increase the total amount available to all.
Trademarks don't really affect that, that's why I don't like the term IP. Trademarks simply say you can't present yourself as others, not that you can't use any kind of information.
Irrelevant. If you haven't told anybody, they have to violate your rights to your property (stealing the plans of the invention) or to your liberty (coercing you in some way to tell them your plans) to obtain your invention.
The whole point of copyright and patents¹ is not to protect your right to the invention, but to give you the right to prevent others from using their legally obtained copies of your invention as they see fit.
¹ I don't like the term IP; see https://www.gnu.org/philosophy/not-ipr.html