At the very least a C++ program can be written using nothing more than a plain-text editor and a C++ language compiler and corresponding linker. However, an integrated development environment (IDE) that supports some variant of C++ is generally much easier to work with.
The best programs are written by humans, not by softwares.
Some C programs can be compiled in C++, yes.
There are very few applications of any note that aren't written in C++ (or some combination of C++ and C). Even the Java virtual machine required to interpret Java programs is written in C++.
Yes.
Writing programs in it.
Writing computer-programs in it.
Server side programs can certainly be written in C. They can be written in any language that the environment supports.
Yes.
C++ compiler, obviously, a C compiler won't do.
Human activity that ends in producing C++ programs.
Any thing and everything. As many as needed.
Device drivers.