<p>This manuscript focuses on the well-posedness, existence, and uniqueness of solutions to abstract second-order neutral integro-differential equations incorporating state-dependent delay in a Banach space. Based on the analytical framework of cosine families theory and fixed-point theorems, we state the assumptions ensuring the existence of mild and classical solutions. This study also explores the stability properties and continuous dependence of solutions on initial conditions, contributing to the well-posedness of the system. Additionally, we provide sufficient conditions under which the solution exhibits regularity properties. An application is presented to demonstrate the theoretical findings.</p>