English distinguishes between "further" and "farther" based on whether the idea being discussed is abstract or physical. "Farther" is kept strictly for literal, measurable distance, like miles or steps, while "further" is used for abstract extensions such as more information, more discussion, or more detail.
The sentence asks for "details," which is an abstract noun about information, not a physical distance. This immediately rules out "farther." "Faster" is unrelated in meaning altogether, it describes speed, and speed has nothing to do with requesting information. "Furthur" is not a standard English word, just an incorrect spelling that sometimes appears by mistake.
Because the request is for more information rather than physical distance, the grammatically and semantically correct word is "further," confirming option 2 as the answer.