They will probably survive with the screen open in the 30's (many people on here do it), but I wouldn't...why make their life more difficult. They can't move below about 45 degrees, and the brood need over 90 degrees, so why leave the window open when they are busy trying to build the house. If I misunderstood, then you are fine. As far as syrup intake, some hives take alot, some don't...I wouldn't worry about it. I have new hives that I need to replace a quart a day, others a quart a week, so don't worry about that. Also, you will see tons of dead bees over the next month, they make packages out of all ages of bees and many only have a few weeks of life left...they are just in there to get you started. It will tip the other direction after about 40 days when you get a couple of brood cycles hatched. Finally, the queen will be fine...they don't need a hole to eat through the candy, it just speeds up the process. Good luck with your bees.