Keep in a dry dark place. If the garlic sits in sunlight, it will start to sprout!
Keep in the chiller drawer of your fridge. If you want to ensure your spinach stays super great for a long time, take out of plastic bag and immerse the spinach in a cold water bath. Let the spinach sit in the cold water bath for 2-3 minutes. Take out of bath and shake or spin dry. Put in a plastic bag (use the one it came in!) and leave the top of the bag slightly open to allow the leaves to "breathe" or poke tiny holes in the bottom of the bag.
Winter Squash (acorn or spaghetti)
Keep in a dry place. Your countertop is fine!
Should be fine in your chiller drawer of the fridge. Even though there's some mud, that will be okay for a day or two. If you want to make sure the carrots last a long time, take out of biodegradable bag and place in water bath. Let the water dissolve some of the residual mud and then, using your hands, rub off the leftover mud. Place in plastic bag. Store in chiller drawer.
Use these onions as soon as you can and keep in a dark dry spot.
Place in cold water bath and let sit for a minute or two. Place in plastic bag with the top open or poke small holes in the bottom so the leaves can "breathe". When you're ready to eat, tear off no more leaves than you need. Keep remaining head in plastic bag. Note, the moment lettuce is torn, it starts to degrade, so only break off enough leaves that you know you will eat!
If you're not going to use relatively soon, place in freezer. Otherwise, cornmeal is fine in the fridge. It is recommended to store in a plastic or glass container if you want to keep it in your cabinet.