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This is referred to as "crumbly fruit." Occasionally raspberry canes bear crumbly berries that literally fall apart when you pick them. Viruses and other diseases, poor nutrition, weather conditions, and pesticide damage can cause crumbly fruit. Some cultivars are more susceptible to crumbly fruit than others. Keeping plants generally healthy is the best way to reduce crumbly fruit. If the problem persists, consider eliminating your raspberry plants and replanting with new nursery stock in a different location.

This article should help: https://www.gardeningknowhow.com/edible/fruits/raspberry/propagating-raspberries.htm

They are definitely suffering from shock, especially due to heat stress. In conditions like yours, they should be watered twice a day. A translucent shade cloth can also help with afternoon shading to keep them cooler in these extremes. Other than that, there's really little you can do.

To determine if your plants are still alive, this article will help: https://www.gardeningknowhow.com/plant-problems/environmental/how-to-tell-if-a-plant-is-dead-and-how-to-recover-an-almost-dead-plant.htm

It is hard to say. Raspberry plants can be sold bare-rooted and they do just fine when planted. But, some of those TV offers don't come from the best of sources. Factors such as the care they received when removed from the soil, put into dormancy and when shipped can make or break a bare root plant's success.

In the future, I would recommend paying a little more for buying from reputable nurseries. The long term health of the plant will be better and you will be less likely to end up with a dead plant. Plus, most reputable nurseries will have a 1 year, money back guarantee on the plants they sell.

It is probably getting too much nitrogen and too little phosphorus. Add some bone meal to increase phosphorus. This article will help:
https://www.gardeningknowhow.com/garden-how-to/soil-fertilizers/phosphorus-plant-growth.htm

It is possible that there are air pockets in the soil that are affecting the roots ability to take up water. I would tamp firmly on the root balls to help collapse any air pockets. They may also have a fungal disease, so I would treat the plants with a fungicide as well.