Tsunami earthquakes are a type of shallow subduction zone events that rupture slowly (<1.5 km/s) with exceptionally long duration and depleted high frequency radiation, resulting in a large discrepancy of Mw and Ms magnitudes and abnormally large tsunami along coastal areas. Heterogeneous fault frictional properties at shallow depth have been thought to dominate tsunami earthquake generation. Some recent studies propose heterogeneous upper-plate material properties determine rupture behavior of megathrust earthquakes, including characteristics of tsunami earthquakes. In this study, we use a recently developed dynamic earthquake simulator to explore tsunami earthquake generation and systematically examine roles of upper-plate material properties and fault frictional properties in tsunami earthquake characteristics in a physics-based framework. For heterogeneous fault friction, we consider isolated asperities with strongly velocity-weakening properties embedded in a conditionally stable zone with weakly velocity-weakening properties. For heterogeneous upper-plate properties, we consider a generic depth profile of seismic velocity and rigidity constrained from seismic surveys. We design a set of models to explore their effects on tsunami earthquake generation and characteristics. We find that the conditionally stable zone can significantly slow down rupture speeds of earthquakes that nucleate on asperities to be < 1.5 km/s over a large depth range (1-20 km), while heterogeneous upper-plate properties can only reduce rupture speeds to be ~1.5-2.0 km/s over a narrow depth range (1-3km). Nevertheless, heterogeneous upper-plate properties promote cascading rupture over multiple isolated asperities on the shallow subduction plane, contributing to large tsunami earthquake generation. We also find that heterogeneous friction dominates normalized duration and high-frequency depletion in tsunami earthquakes. In addition, the effective normal stress on the subduction plane, which affects fault frictional strength, significantly influences the characteristics of tsunami earthquakes, including long normalized duration and low stress drop.