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This should be fine, provided the walnuts are not black walnut trees, which are allelopathic. You do not need another type for pollination.

Yes. This article will help with that: https://www.gardeningknowhow.com/edible/fruits/blackberries/propagating-blackberries-cuttings.htm

These two plants should not be grown together, as they are prone to the same pests and diseases. Here are some articles on growing blackberries which you may find helpful: https://www.gardeningknowhow.com/edible/fruits/blackberries/growing-blackberry-bushes.htm, https://www.gardeningknowhow.com/edible/fruits/blackberries/blackberries-not-fruiting.htm

You can plant them within the same area as long as they are all domesticated varieties and certified virus free. Do not plant wild varieties of any kind of berry near domesticated ones as the wild varieties may carry diseases. Wild blackberries can carry fungus and viruses that can make your raspberries sterile (more information here: https://www.gardeningknowhow.com/edible/fruits/blackberries/blackberries-not-fruiting.htm).

It probably succumbed to shock. These articles should help: https://www.gardeningknowhow.com/plant-problems/environmental/learn-how-to-avoid-and-repair-transplant-shock-in-plants.htm, https://www.gardeningknowhow.com/plant-problems/environmental/how-to-tell-if-a-plant-is-dead-and-how-to-recover-an-almost-dead-plant.htm

Bt (Bacillus thuringiensis) is effective against almost all caterpillars/worms. Neem oil is effective against almost all the rest of the pests it could be. I would try the Bt first.