Dark energy and dark matter, two subjects of basic physics, have received a lot of attention in the 21st century. From the observational point of view, the interaction between dark energy and dark matter can significantly affect cosmological distances. This gives rise to the possibility of indirectly detecting such interaction through high-redshift cosmological probes. Theoretically, the introduction of interaction between dark energy and dark matter can assist in alleviating the coincidence problem of the standard cosmological model ($\Lambda$CDM model). Furthermore, this can provide a new method of studying the properties of dark matter particles. In this paper, based on the latest observations of multiple measurements of quasars (X-ray+UV quasars acting as standard candles, compact radio quasars acting as standard rulers) covering the redshift range of $0.04~<~z~<~5.1$ and baryonic acoustic oscillation between ($0.38~<~z~<~2.34$), we investigate the observational constraints on a variety of interacting dark energy models ($\gamma_d~$IDE model, $\gamma_m~$IDE model) and other cosmological models ($\Lambda$CDM model, XCDM model). The results provide us with a quantitative analysis of the possible interaction between dark energy and dark matter, as well as the possible range of the mass of dark matter particles. The joint analysis shows that: (1) Multiple measurements of quasars can provide more stringent constraints on the interacting dark energy models, which can further strengthen the potential of quasars acting as effective cosmological standard probes at higher redshifts; (2) In the framework of both $\gamma_m$IDE model and $\gamma_d$IDE model, the quasar data supports possible conversion of dark energy into dark matter at high redshift, which alleviates the coincidence problem to some extent. We also found that the interaction term is of a small value, which demonstrates the negligible interaction between dark matter and dark energy; (3) In the framework of $\Lambda$CDM model, which has shown the best consistency with quasar data, the density parameter of matter in the Universe is constrained at $\Omega_~m=0.317^{+0.007}_{-0.007}$, with the best-fit Hubble constant $H_0=68.177^{+0.497}_{-0.505}$ at 68.3% confidence level. These findings are consistent with the recent microwave background radiation (CMB) measurements from the Planck satellite; (4) If dark matter in the Universe exists in the form of scalar-field dark matter with $Z_2$ symmetry, we obtain the range of the mass of dark matter particles as $56~{\rm~GeV}\lesssim~m_S\lesssim~63~{\rm~GeV}$ or $m_S\gtrsim450~{\rm~GeV}$, based on the dark energy-dark matter coupling term from multiple measurements of quasars. Such conclusions agree well with the latest experimental results aimed at the direct detection of dark matter particles.
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