Rhubarb should last for about 4 days in the refrigerator's crisper. Keep it tightly wrapped in plastic. If you want to store it long term, wash, cut into the desired length, and place in an airtight container. It will keep in the freezer for about 9 months.
Fennel will keep for about 5 days if you store it in a plastic bag in the refrigerator crisper. Unless using fennel within a couple of days, trim off the stems and store them separately so they don't leach moisture from the bulb.
This squash should keep for up to 4 weeks when stored in a plastic bag in your refrigerator's vegetable drawer.
These fruits should keep for at least 2 weeks, and up to a month, when stored in a paper bag in your refrigerator's vegetable drawer. If you plan to use them within a couple of days, they will be fine on the countertop.
To store okra, wrap it in a paper towel and tuck inside a paper bag, then place in the least cool section of the refrigerator. Try to use it soon after purchase, as okra is quite perishable. It should keep for 3 or 4 days.