We carried out extensive first-principles modeling of microscopic structural, vibrational, electronic properties and chemical bonding in hydrogenated amorphous silicon (a-Si:H) in a wide range of hydrogen concentration and preparation conditions. The theory has been compared with experimental results to comprehensively characterize this semiconductor material. The computer modeling includes ab-initio Molecular Dynamics (MD), atomic structure optimization, advanced signal processing and computer visualization of dynamics. We extracted parameters of hydrogen and silicon bonding, electron charge density and calculated electron density of states (EDOS) and hydrogen diffusion. A good agreement of the theory with various experiments allowed us to correlate microscopic processes at the atomic level with macroscopic properties. Here we focus on correlation of the amorphous structure of the material, atom dynamics and electronic properties. These results are of increasing interest due to extensive application of a-Si:H in modern research and technology and to the significance of detailed understanding of the material structure, bonding, disordering mechanisms and stability.