Falls down stairs are an all too common cause of head injuries and other serious injuries. Therefore properly install stair gates at the top and bottom of all stairways, and always ensure they are properly closed. The reason for installing stairgates at the bottom of staircases is to ensure that a child can't climb up the stairs then fall back down.
Window locks and guards
Ensure that all windows are secure and locked.
Better yet, install window-guards that stop children from falling out, but which can also be opened in case of fire.
If secure windows are your landlord's responsibility, insist that necessary maintenance be done immediately.