Does it alter their nutritional content or medicinal values of the fruits stored in the refrigerator?

As far as I am aware, both fruit and vegetables start to lose some of their vitamin and mineral content the moment they are picked, but at a very slow rate. So, any kind of storage will result in a little less nutrition than when eaten straight from the plant.

The main problem with fruit is that once they are separated from the parent plant they are designed to begin decaying in order to release the seeds which will eventually multiply the species. They decaying process is then accelerated by moulds, fungi and other species which use the nutrients to reproduce their own species.

I find that certain berry fruits seem to decay faster in the fridge than at room temperature, but why this is I dont know. This is especially true with blackberries, raspberries and strawberries.

With larger fruits and those with harder, thicker skins a cold environment does slow their deterioration rate, but then some of the sugars in the fruit will slowly begin to ferment. This will alter the nutritional structure of the fruit anyway, and may even increase the presence of certain nutrients while other decrease. It is a very complex subject.

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Not at any significant level. In studies, even when fruit was cut and refrigerated it only lost 5 to 10% of vitamins after 6 days of storage. Even this small loss is insignificant.

Some fruits however will not ripen once chilled and in general ripening of fruits will be delayed greatly by cold storage.

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It can for some, like tomatoes(yes they are a fruit). The cold destroys the flavor enzyme in tomatoes and it does NOT come back when the tomato is returned to room temperature. Storing in the fridge is okay for most fruits but not necessary unless you prefer cold fruit and have lots of room in your fridge. Most are NOT kept in coolers at the store at all and are sold at room temperature.