I'm so sorry for your loss Chey's mom.
Pookietooth, the Redi Blinds are very cheap. We have ours up now and they work well and look decent. You could put the ones that come with your unit into storage for the time being and replace them before you move out if your landlord isn't willing to provide you with something safer.
About the dresser. Actually, ours isn't mounted to the wall yet. But it should be. We have taken all of the knobs off. Simon can't open any of the drawers this way. If the bottom drawer is open and he climbs into it and jumps a bit or tries to use this as a ledge to climb higher, it could easily fall over. We watch him in the bedroom very carefully and will mount it to the wall soon. Before we know it he'll know how to pull the drawers open without the knobs. Call me paranoid if you want! It will take 10 minutes of my life to attach the dresser to the wall. T.v.'s in entertainment units pose a similar danger btw, though perhaps worrying about this is foolish too? I don't think so!