The thread title is, "What is a browser?"; you've asked multiple questions, hence multiple answers.
All of the functional support is implemented using C++(or other language) and rendering( graphical interface components, images, fonts ,ect ect) is DirectX/OpenGL, so repeating myself it's just a program written in C++(or other) and OpenGL/DirectX.
After having read the above, can you confirm that, or am I missing/misunderstanding something?
They are normal computer programs, yes. Just like Microsoft Word or Microsoft Excel. Browsers that are modern-day feature-complete like Firefox are also fairly complex, just like Microsoft Word and Microsoft Excel.
'Normal computer programs' can be programmed in any language that can generate regular executables. So, yes, C++ is a likely bet for Firefox. It could've just as easily been coded in Python or Java or C#.
You are misunderstanding DirectX and OpenGL. While they likely do use DirectX and OpenGL on some level, they don't have to. They could've just as easily done their rendering in SDL or any other graphics library. Infact, Firefox used to use Cairo, and now uses a different API. Technically, Microsoft Windows could (and maybe does) still use DirectX behind the scenes to visually present the windows, but most programmers wouldn't say Firefox "uses" DirectX.
Technically, Firefox could use Cairo, with an OpenGL backend, using Angle to convert the calls to DirectX, running in WARP software mode, rendering to a Direct2D window, that presents the window behind the scenes using DirectX.
I'm not saying that this is what is actually happening, but such things are possible. So "technically" Firefox could be using, calling, or interacting with on some level DirectX, but it still wouldn't have to be "written in" DirectX.
DirectX is not a requirement, though the Operating System (or other APIs you might be using) may happen to use DirectX behind the scenes.