Install safety bars in the windows. Do not rely on someone to leave the windows closed, only open them a little, etc. You can get window guards in any hardware store, Home Depot or Lowe's. They screw into the window frames and have a quick-release mechanism in case of fire. If your parents bought the condo they should have no problem with being able to install these as they are a safety item and inside their house. If they are renting, they may need the landlord's permission but they should have no problem getting agreement because they are a safety item.
I lived in a 3rd floor apartment for a couple of years when my oldest was a toddler and was very paranoid about fires as well as widow falls because you can't just jump out of a 3rd story window if the doors and stairwells are blocked. So I made sure that I had those fire escape ladders (one in every bedroom, stored under the bed) as well as fire extinguishers, smoke alarms, and fire blankets (which can be used to put out small kitchen fires, etc.). I hope I didn't make you more nervous, but I think that these are legitimate concerns for living above the 2nd floor and having these items made me relax about living higher up.