This car can be purchased in the Ford section of Brand Central for 450,000 Credits. It can also be obtained by signing a Manufacturer's Series contract with Ford, which is valid for one Manufacturer's Series season and allows the car to be used in Manufacturer's Series races.
A GT3 based Ford Mustang does exist in real life, called the FR500GT3, however it is based on a previous generation model. There is also a similar-looking Mustang GT3 race car made by MARC Cars, an Australian racing constructor.
In pre-release screenshots of the game, there were Gran Turismo logos on the car's doors. The car's fuel/lubricant sponsor was also replaced from Total to Castrol in the final game.