Understanding the Physics of thermonuclear explosions of a White Dwarf star (WD), so called Type Ia Supernovae (SNe Ia), provide a playground for modern physics, computational methods, and are a key to modern cosmology. We identify new and investigate a variety of observational signatures of underlying physical processes related to the thermonuclear runaway, the flame propagation and the environment. Being intrinsically multi-dimensional phenomena, probing the physics requires multi-dimensional radiation-hydrodynamics and MHD simulations. For this task, we developed and employed methods for photon transport for the X-, gamma- and of low energy and of positrons under non-LTE conditions. We identify signatures in the light curves and spectra, in particular, line profiles and polarization spectra. Consistent treatment of high energy processes is critical. Therefore, our framework and results can be used directly a variety of scenarios for SNe Ia including merging WDs and explosions of sub-Chandrasekhar mass WDs. Current simulations have limitations but, nevertheless, when combined with recent JWST and VLT observations solutions emerge to many of decade old problems on the ignition process, flame physics and thermonuclear explosion.