We present calculations on electronic band structures and topological properties of the flat band of twisted bilayer WSe2 with twist angle near 1°, by using the effective continuum model under different heterostrain, pressure and vertical electric field. We find that the first valence band exhibit a narrow bandwidth and can be efficiently modified by heterostrain, where a much narrower bandwidth of this flat band can be achieved over a wide range of strain magnitudes. The energy gap between the first two valence bands is reduced by heterostrain while it is significantly enlarged under pressure and vertical electric field. Furthermore, the applied vertical electric field leads to topological transition in each valley for the first valence band. We give a feasible experiment proposal to reveal this phenomenon. Our results serve as a theoretical guide for exploring emergent correlated electron physics and topological physics in this versatile moiré superlattice system.