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The variability characteristics of active galactic nuclei (AGNs) serve as a powerful diagnostic tool for probing the physical mechanisms underlying accretion processes and jet formation in supermassive black holes. Using long-term optical time-domain monitoring data from the Zwicky Transient Facility, this study applies the damped random walk model to fit the light curves of radio-quiet AGNs, enabling the extraction of their optical variability amplitudes and characteristic timescales. We investigate the origins of optical variability in radio-quiet AGNs. The main findings are as follows: (1) There is a significant correlation between variability amplitude and Eddington ratio; in contrast, variability amplitude is not significantly correlated with radio luminosity. These results indicate that the optical variability of radio-quiet AGNs is primarily driven by the Eddington ratio, rather than relativistic jets. (2) The relationship between variability amplitude and Eddington ratio in radio-quiet AGNs is highly dependent on the accretion mode. For the efficient accretion mode, the variability amplitudes of radio-quiet AGNs are inversely correlated with the Eddington ratio; in contrast, for the inefficient accretion mode, these variability amplitudes are positively correlated with the Eddington ratio. (3) A significant correlation between optical variability amplitude and X-ray luminosity is observed for radio-quiet AGNs. This finding may support a scenario in which variations in UV/optical emission and heating of the X-ray corona are jointly regulated by magnetohydrodynamic turbulence within the accretion disk.

Dual active galactic nuclei (DAGN) mark the observable stage of massive black hole (MBH) pairing during galaxy mergers and are the progenitors of the MBH binaries that generate low-frequency gravitational waves. Using the large-volume ASTRID cosmological simulation, we construct mock DAGN catalogs tailored to the selection functions of current (COSMOS-Web and DESI) and forthcoming (Nancy Grace Roman Space Telescope (Roman) and Lynx X-ray Observatory (Lynx)) surveys, enabling direct comparisons between simulations and observations. With realistic observational selections, ASTRID reproduces the observed dual fractions, projected separations, and host-galaxy properties across redshifts. We predict a substantial population of small-separation (<5 kpc) duals that remain inaccessible to current surveys, demonstrating that the apparent paucity of subkiloparsec systems in COSMOS-Web is primarily a consequence of observational selection rather than an intrinsic absence. Following each simulated dual to coalescence, we show that DAGN are effective tracers of MBH mergers: ~30%--70% merge within ≲1 Gyr, and 20%--60% of these mergers produce gravitational-wave signals detectable by the Laser Interferometer Space Antenna (LISA). Duals observable with Roman and Lynx are the progenitors of ~10%--50% of low-redshift LISA sources and contribute ~30% of the PTA-band stochastic gravitational-wave background. We further identify massive green-valley galaxies hosting moderate-luminosity active galactic nuclei (AGN), together with massive star-forming galaxies containing bright quasars at z > 1, as the environments most likely to host imminent MBH binaries. These results establish a unified cosmological framework connecting DAGN demographics, MBH binary evolution, and gravitational-wave sources, while identifying high-priority targets for coordinated electromagnetic and multimessenger observations in the coming decade.