In this paper, we present an analysis framework for description of nonlinear, self-consistent laser-plasma evolutions during propagation of a short intense laser pulse in a high-density sub-critical plasma (the pulse length exceeds the plasma wavelength). In this context, the pulse evolutions are attributed to the wakefield induced self-modulation and destabilization via parametric exponentiation of the initial noise content. The self-consistent plasma evolutions are formulated in terms of used-to-be motion constants in the absence of pulse evolutions. This proves very useful both in uncovering important plasma dynamics during self-modulation and also in facilitating the instability studies in the strongly nonlinear regime through refinement of unstable plasma perturbations. General analytical solutions, at arbitrary pulse conditions, are derived for self-modulation, indicating that the envelope evolutions are driven by the induced spatial frequency-chirp. Also, these results state that the envelope attains fine modulations which produce long wavelength low-frequency modes via beating the carrier mode. The plasma wave variations are found to convect and amplify away from the pulse front. Regarding parametric instability, we assess different scattering regimes at different pulse shapes and peak intensities, manifesting anomalous behaviors ranging from wild positioning of the Stokes wave in dispersion plane to broadening in the scattered spectrum and halting the instability. Our analyses are assisted and verified by numerous fluid and particle-in-cell simulations. Based on our results, we discuss phenomena like the pulse breakup and its different regimes, and assisted particle acceleration in the presence of pulse evolutions.