We analyse some open debates in cosmology in the light of the most updated quasar (QSO) sample, covering a wide redshift range up to z ∼ 7.5, combined with type Ia supernovae (SNe) and baryon acoustic oscillations (BAO) data. Indeed, extending the cosmological analyses with high-redshift data, such as QSOs, is the key to distinguishing between different cosmological models that are instead degenerate at low redshifts, and allowing a better constraint on a possible dark energy (DE) evolution. Also, we discuss different combinations of the BAO, SNe, and QSO data to understand their compatibility and their implications for the non-flat Universe and extensions of the standard cosmological model. Specifically, we consider a flat and non-flat ΛCDM cosmology, a flat and non-flat DE model with a constant DE equation of state parameter (w), and four flat DE models with variable w, namely the Chevallier-Polarski-Linder and Jassal-Bagla-Padmanabhan models, and an "exponential" and "rational" parameterisations. We find that a joint analysis of QSO+SNe with BAO is only possible in the context of a flat Universe. Indeed BAO confirms the flatness condition assuming a curved geometry, whilst SNe+QSO show evidence of a closed space. We also find that the matter component, Ω M,0 , is fully consistent with Ω M,0 = 0.3 in all the data sets assuming a flat ΛCDM model. Yet, all the other analysed models show a statistically significant deviation at > 3σ from this prediction by making use of the SNe+QSO sample, which remains still significant (2-3σ) with the combined SNe+QSO+BAO data set. In the models where the DE density evolves with time, the SNe+QSO+BAO data always prefer Ω M,0 > 0.3, w 0 < −1 and w a greater, but statistically consistent, than w a = 0. This DE phantom behaviour is mainly driven by the contribution of SNe+QSO, while BAO are closer to the prediction of the flat ΛCDM model (also due to their large uncertainties).