Linux does have the idea of an executable binary file. However, linux typically doesn't use file extensions in the same manner of which Windows does which is why you don't see .exe files. You can still program in C/C++, compile your code into a binary, and run it. The most popular compiler out there for linux is
gcc (Gnu Compiler Collection) which can compile a bunch of different languages. There is also java implementations from Sun and others.
.o (object) and .so (shared object) files are examples of library code. .so files closely resemble dll files in windows.
As far as IDE's go, there are bunches of those too, but I'll let somebody else suggest one because I pretty much stick to text editors.
