Matter bends space-time with the effect of gravity.
Yes - we think. Just as matter has an inertial mass that 'creates' gravity, so does antimatter. Antimatter has the same energy as matter and as energy is mass and vice versa there is no reason why antimatter should not behave like real matter. This has never been put to the test however. There is a possibility that there might be a few subtle differences in the way the antimatter behaves.