Seriously? Yes. They all have seeds...or a seed, which makes them a fruit, botanically speaking. Is this important to your life? Not really, except as bar trivia or as a way to categorize them that is not totally unreasonable given the way we eat them.
Like many of their sweet fruit cousins, most vegetables-that-are-actually-fruits are best in the summer time (with the exception of winter squashes). Also similarly to the rest of the fruit family, these foods will have the most delicious flavor when grown locally, picked recently, and not shipped around in the world in climate-controlled containers. Try buying in-season and from local farmers whenever possible, especially tomatoes. The obvious exception is avocados, unless you're lucky enough to live in an avocado-friendly climate, which are easiest to buy when slightly less-than-ripe (still a bit firm to the touch) and let them ripen at home.
You can eat them all raw or cooked in a myriad of ways, except eggplant and winter squash which are best cooked. We tend to treat the wide variety of winter squashes more like root vegetables when cooking due to their hard, but often sweet texture, so feel free to examine those recipes for additional options.
You might be tempted to do it, thinking they'll last longer...but don't refrigerate tomatoes! In fact, try not to refrigerate any of the above fruits. They grow best in hot weather and will taste best outside of the fridge. I sometimes will briefly stash the other fruits in the fridge to extend their life just a bit, but then try to eat them as soon as possible. Winter squashes should be stored somewhere cool, but also can live in the fridge for a few days if necessary.
Wrinkled fruits are generally totally fine to eat. You may not want to put wrinkled tomatoes or peppers in a raw salad, but they will roast up beautifully. Zucchini and summer squash might lose their firmness and vibrancy after a few days, but you can still cook them in a stir-fry or Fried Rice. Once fruits get mushy or moldy though, to the compost they go.