We perform tunneling measurements to study the low-energy states of quantum dots formed in semiconductor nanowires and coupled strongly to a superconductor. Although non-topological in nature, these states, commonly known as Andreev bound states (ABSs) or Yu-Shiba-Rusinov states, hold relevance in the context of topological superconductivity. Indeed, ABSs are expected to evolve towards Majorana modes across a topological phase transition when in the long wire limit. In addition, understanding the ABS spectra of hybrid nanowire devices is important for the interpretation of experiments directed at the observation of Majorana modes. In this work, we perform a detailed study of the sub-gap states of a tunable spin-½ quantum dot. We first exploit the ability to control the coupling between the dot and the superconductor to explore the phase diagram of the possible ground states of the system: a spin singlet or a magnetic doublet. By applying external magnetic fields, we study the spin texture of the Andreev states and demonstrate zero-bias crossings resulting from parity-changing phase transitions.  Finally, we evaluate the impact of mesoscopic tunnel probes in the detection of ABSs. We show that the non-trivial density of states of such probes yields numerous replicas of the sub-gap states, thereby leading to crowded Andreev spectra.