The word backside is an informal word meaning bottom- the part of your body that you sit on.
For more information please turn to your backside
The speakerwriter probably meant 'turn to face backwards'turn to the back of the letter, but misunderstood what backsidebackside means. It is not ungrammatical, but would probably be impossible unless you are a yoga expert.
The response is also grammatically correct but very informal, and: the spelling is an attempt at an east London accent, and there should probably be a comma after Oh and before brilliant. "Bloomin 'eck" is a euphemism for "bloody hell", and "all right" means "satisfactorily".