I have compiled a simple executable application written in C, using the arm-linux-gnueabi compiler for ARM.
How to run it on device?
Assuming that I have two devices for test it:
If is not possible run it on the current operating system, then how to format the device and put my kernel instead of Android/Linux?
An application is typically built to run on top of an operating system. An operating system is typically built to run on top of hardware. Keep this in mind.
Running your application instead of Android/Linux implies that your application is a operating system of some sort. If you didn't write or include explicit code to control the hardware chips in the device, then you are only asking the wrong question, you should ask "I've wrtten an application in C, now how do I run it on my phone's operating system." If you did write or include explicit code to control the hardware chips in the device, then you did ask the right question (but some of the details seem off). This style of development happens a lot with the arduino/PIC/embedded ARM community.
Assuming you are not doing embedded development, the application must be compiled with some understanding of what the operating system offers (against the operating system's available api's) which generally makes them incompatible with other operating systems. This means the first step is to determine what operating system you are targeting, and obtain it's development suite. Once you have that, assuming that it supports C code (as most do), the suite will recompile your source code in a format that is both compatible with the CPU of the device and the API of the operating system on the device.
Small devices like phones typically run operating systems that have a tiny fraction of the features of a PC, so be prepared for fewer convenience features, and possibly "missing" libraries. That said, if you do get it to compile, typically you then hook the device up with the supported "bus" (USB is very popular), and save the program on the device (which sometimes involves sending "development / debugging" codes across the bus, and the development suite does this for you).
If everything worked well, you can then launch your program from the phone. If the program misbehaves and renders the phone inoperable, each development suite / phone has specific instructions on how to recover or reload a fresh operating system.
Here are resources for a few well known platforms (and percentages of the phones using them)
Note that these measurements are like most surveys, while they attempt to be random and unbiased, they are prone to measurement error and sampling error, so the numbers are more useful as relative indicators than absolute values.
