Name the temple having "scenes from the Ramayana sculpted on the inner walls of the shrine" in the Vijayanagara empire?

Hazara Rama Temple

The correct answer is Option (4) → Hazara Rama Temple

The temple with "scenes from the Ramayana sculpted on the inner walls of the shrine" in the Vijayanagara empire is the Hazara Rama Temple. 

This was probably meant to be used only by the king and his family. The images in the central shrine are missing; however, sculpted panels on the walls survive. These include scenes from the Ramayana sculpted on the inner walls of the shrine.