This paper studies the effectiveness of production of Alfvén waves in the solar atmosphere through the processes of mode conversion, taking into account several new effects that have not been considered before. We perform simulations of wave propagation and conversion from the photosphere to the corona. Both magnetic field and plasma parameters are structured in the form of small-scale flux tubes with characteristic scale significantly below the wavelength of the waves. The waves are allowed to dissipate through the ambipolar diffusion (AD) mechanism. We use an analytical magneto-static equilibrium model, which provides the AD coefficient values at the lower end of what is expected for the quiet solar regions. This work extends the simplified study of mode conversion by Cally and Cally & Khomenko to the case of warm, partially ionized, and structured plasma. We conclude that interaction of waves with the flux tube ensemble produces a discrete spectrum of high-order harmonics. The scattering is a linear process: however, the nonlinear effects have considerable influence upon the amplitudes of the harmonics. The magnetic Poynting flux reaching the corona is enhanced by about 35% and the reflection of waves at the transition region is decreased by about 50% when the flux tubes structure is present, relative to the horizontally homogeneous case. The energy flux of Alfvén waves exceeds that of acoustic waves at coronal heights. Ambipolar diffusion decreases the magnetic Poynting flux in the corona because the fast waves entering the transformation region at chromospheric heights are degraded and have lower amplitudes. The effect of the enhancement of Alfvén wave production due to interaction with flux tubes is independent of the numerical resolution, while the effect of the AD is resolution-dependent and is not converged at the 10 km resolution of our best simulations.