Fully titled Open Graphics Library, it is a cross platform, cross language application programming interface, or API. The interface typically serves to interact with a system's GPU (graphics processing unit) in order to achieve hardware accelerated rendering of 2D and 3D vector graphics. It has been around since January of 1992.
Yes and no. A new API named Vulkan is presently being developed to replace this GL and will not be backwards compatible with earlier versions. In that respect, it is dead. However Vulkan is still being developed, and OpenGL still has new releases being put out on a regular basis.
There is no cost to using this graphics library, though it should be noted that you will have to know what to do with it. A library is not an application that can be loaded up. It will require in depth programming knowledge to make use of these graphics libraries.
The libraries themselves are not "hard", however it is not really the correct question to ask. The libraries make creating graphical programs easier, but it is those programs which you create that determine the difficulty of the project. Regardless of the project, however, these libraries should make life somewhat easier.
Though used in game engines, such as the free, open source OGRE engine, these libraries are merely an API to interface with the GPU of a system, and not a game engine themselves. The ability to interface with a range of graphics hardware initially made these libraries invaluable to developers.
OpenGL is not a programming language itself, though it is written in C. It is actually a set of libraries that serves as an API to interface between software and a computer's graphics hardware. It is not necessary to exclusively write in C in order to use these graphics libraries.
Unity supports a number of different graphics libraries, including this one. In fact, it is the default renderer when using Mac and Linux systems. On Windows, the default is Direct3D, and a setting will need to be changed to use GL instead. But yes, Unity3D does use these graphics libraries.
As this is a collection of libraries, rather than a standalone software package, individual compatibility with Windows 10 does not really apply. The libraries will be used with the hardware's drivers. If that hardware has drivers for Windows 10, or drivers that work with Windows 10, then these libraries will work with Windows 10.
As part of the drivers for various graphics hardware, yes, these graphical libraries come with Windows. It is not Windows that requires these libraries, but the hardware on which Windows is running. However Windows often carries the drivers for this hardware, so in that respect it could be considered to come with Windows.
From a particular version of OS X onward, these graphic libraries were included on the installation media for the OS. There has not historically been as much use of the libraries on Mac, however this is likely more to do with a lack of Mac video games in general.