In this thesis we have studied the stability of ions that are stored in isolation using different laser probing techniques. Laser photodetachment threshold spectroscopy (LPTS) was used for high-precision measurements of electron affinities, an inherent property of atomic and molecular systems important for fundamental research and numerous applications, e.g., for antimatter research or accelerator-based nuclear dating. The measured electron affinities in this thesis include atomic cesium ¹³³Cs and oxygen ¹⁶O, and two fullerenes molecules, C₆₀ and C₇₀. In addition, we have studied the cooling dynamics of ions, relevant to astrophysics, in new time domains and in unprecedented detail. Here, we implement action spectroscopy techniques in DESIREE, a cryogenically cooled electrostatic ion-storage ring with outstanding vacuum conditions. The studied molecules include polycyclic aromatic hydrocarbons (C₁₀H₇CN⁺, C₁₈H₁₂⁺), carbon chains (C₄H⁻, C₆H⁻) and fullerenes (C₆₀⁻ and C₇₀⁻ ). These cooling dynamic experiments were aided by ab initio calculations and numerical simulations in order to unveil the importance of the different relaxation mechanisms that internally excited ions undergo, which determine their survival probabilities. The results presented in this thesis may play an important role for astrophysical modelling, which aims to deepen the understanding of the evolution of molecules in outer space.