It depends on the editor.
You could, if you had conio.h in linux, but you don't have, that's why.
Simply any text edittor can be used to write C program. To compile the .c file saved, Linux comes with gcc compiler. In the command line: $ gcc -o outputfile inputfile.c will compile the inputfile.c and create executable outputfile. Other than that there are number of IDEs (i.e. Integrated Development Environment) are available such as Kdevelop, Eclipse etc.
This question cannot be answered without seeing the source program.
C isn't a program, or something you install; it is a programming language for writing software. Linux and most of the programs that run on it were written in C, and a C compiler and libraries are supplied with most systems, or are readily available.
All binaries are launched by simply typing the name of the application.
To program in linux, you just have to pick out a programming language, and use your favorite text editor or IDE to start programming. Most prodominantly, programs are written in C or C++ and can be compiled with the Gnu C Compiler (gcc) or g++ if your program is in an interpreted language, such as perl or python, you just have to make sure you have the interpreter installed.
There is very little difference in the C compiler between Unix and Linux; in some cases (the gcc compiler) it is the same. The differences come in when using system calls; some system calls do not exist in Unix or Linux, although most do. The program I work on compiles the same way (for the most part) between all commercial versions of Unix and several variants of Linux. In other words, the code is fairly portable across platforms.
Different for every C program. For example, linux is an OS-kernel, whilst Apache is a web-server.
C programming is just that no matter if the operating system is Windows or Linux. Operating systems usually have an Application Program Interface that is commonly known as an API. The APIs of Windows will be different than Linux because the operating systems are (very) different.
Search for BGIDEMO.C in your TurboC. There are thousands. Many Unix/Linux graphics programs are written mainly in C or C++, including X itself.
Linux Wine is an open source software program. The Linux Wine software program allows Linux users to run Windows programs on their own devices such as computers.
No. There is no program named "Graphics" for Linux.