We explore tidal disruption events (TDEs) and extreme mass-ratio inspirals (EMRIs) in the co-evolution of massive black holes (MBHs) and nuclear star clusters (NSCs). Over 12 Gyr, we investigate the evolution of the NSC with a mass-growing MBH, as well as the EMRIs of stellar black holes, neutron stars, white dwarfs, brown dwarfs (BD), and low-mass main-sequence stars (MS), along with TDEs involving MSs, BDs, and post-MSs. The evolution of TDE and EMRI rates is generally affected by the cluster's size expansion or contraction, stellar population evolution, MBH mass growth, and the stellar initial mass function. LISA-band EMRIs involving compact objects around Milky-Way-like MBHs tend to have high eccentricities, while those around spinning MBHs preferentially occupy prograde orbits. In contrast, MS- and BD-EMRIs usually have eccentricity and inclination distributions that are distinct from those of compact objects.
