Problem with using pure C code to program default UART (UART0) in Arduino Mega
I suggest to use existing code and copy that or use that.

This is the Arduino HardwareSerial : HardwareSerial.cpp
You can find more code at avrfreaks.net. Click on "Projects", search for "uart" and "usart" and try to find code that is compatible with the ATmega2560. Some projects have buffers and many functions, others are very simple.

The result might not be compatible with other Arduino code (for example with interrupts). Why do you not want to use the Arduino Serial library ?