Abstract: Droplet evaporation on structured or pillar surfaces is governed by gravity, capillarity, vapor diffusion, natural convection, thermocapillary convection, Stefan flow and edge-induced contact-line pinning. In reactor cooling and microgravity thermal management, droplets are often pinned by geometric edges, and their morphology may deviate from the spherical-cap assumption when the Bond number exceeds unity. In this study, the morphology, gas-phase flow, internal circulation, and heat transfer of water and ethanol droplets on a single pillar were clarified to be regulated by gravity orientation, pillar-edge height, and substrate heating. A combined experimental and numerical approach was adopted. Experiments were performed for sessile water droplets, pendant water droplets and pendant ethanol droplets on pillar end faces with different dimensionless pillar heights, and the evolution of droplet volume and profile was recorded by high-speed imaging. A two-dimensional axisymmetric moving-mesh model was established for the liquid and gas domains. The model solves weakly compressible conservation equations and vapor-concentration transport, while incorporating evaporative flux, latent-heat consumption, Stefan flow, Marangoni stress and buoyancy-driven natural convection. A disjoining-pressure formulation represented liquid-solid interactions and maintained contact-line pinning under the constant-contact-radius mode. The model was validated using measured volume evolution and microgravity data. The results show that droplet morphology is determined by gravity and surface tension. Under normal gravity, a sessile droplet is compressed into an ellipsoidal cap with larger curvature near the contact line, whereas a pendant droplet is vertically elongated and exhibits enhanced curvature near the apex and neck region. Under microgravity, the droplet remains closer to a spherical cap with more uniform curvature. As evaporation proceeds, droplet volume and Bond number decrease, surface tension becomes dominant, and gravity-induced differences weaken. The external flow field is driven by natural convection, Marangoni-induced interfacial motion and Stefan flow. For unheated cases, pendant droplets generate stronger external airflow than microgravity droplets, and ethanol droplets induce more intense external gas-phase flow than water droplets. Increasing pillar height weakens the baffle-induced blocking effect and promotes vapor removal, especially when the pillar edge is located upstream of the gas flow. Under heating, buoyancy-driven flow reinforces Stefan flow around sessile droplets, while opposite flow directions around pendant droplets promote vortex formation. Gravity and edge confinement also alter thermal resistance, interfacial temperature gradients and internal Marangoni circulation. Pendant droplets show larger temperature differences and stronger internal flow under unheated or weakly heated conditions, whereas heated sessile droplets exhibit stronger coupling between external and internal convection. Ethanol droplets display a stronger thermocapillary response because of greater volatility and larger temperature gradients. Overall, evaporation on pillar surfaces cannot be described adequately by a purely diffusion-limited model or ideal spherical-cap geometry. These findings provide a basis for optimizing microstructured cooling surfaces and improving evaporation heat-transfer models in reactor cooling and microgravity thermal management.