In this talk we are concerned with the dynamics of a general class of focusing mass-critical nonlinear Schrödinger equations (NLS) with lower order perturbations, for which the pseudo-conformal symmetry and the conservation law of energy can be absent. Two canonical examples are stochastic NLS driven by linear multiplicative noise and deterministic NLS. We show the construction of multi-bubble Bourgain-Wang type blow-up solutions, and the uniqueness in the energy class where the convergence rate is of the order (T-t)^{4+}. The corresponding existence and conditional uniqueness of non-pure multi-solitons (including dispersive part) to mass-critical deterministic NLS is also obtained. The results in particular provide new examples of mass quantization conjecture and soliton resolution conjecture. If time permits, the refined uniqueness for multi-bubble blow-ups and multi-solitons of NLS would be presented.