Suppose a universe with similar physical laws to ours, with the major exception of gravity not existing as we know it, with an analogous force (hereafter called gravity for simplicity) acting as a constant acceleration to the normal vector of an unbounded plane. Given a certain amount of handwavium, a density gradient of material creates layers similar to an Earth-like planet, i.e. molten material, crust, water in some areas, and air. An additional bit of handwavium puts lights in the sky analogous to the sun. Presume an initial condition similar to early Earth, with an atmosphere produced by volcanic outgassing. Then given the appearance of life at an arbitrary point, how quickly would such life propogate outwards from that point, and how quickly would secondary developments, such as the oxygenation of the atmosphere, spread from their respective origins?
EDIT: Include the following additional assumptions. Life begins in primordial oceans similar to on Earth, and that evolution proceeds similarly. Cyclonic weather patterns would not occur due to the absence of rotation, so large scale weather would dissipate more quickly. Tides would result from the same handwavium that puts lights in the sky. Temperature differences from region to region would be more dependant on prevalence of mountains than anything else, but there would still be large scale movements of air and water.
EDIT #2: Tectonic activity is similar to earth, but because of the differing geometry, plate boundaries tend to be mostly straight. Continents would still form but be more angular at their boundaries, and some extreme geography could appear (there's unlimited space for variation after all).