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This article will help with producing more plants: https://www.gardeningknowhow.com/edible/fruits/blackberries/propagating-blackberries-cuttings.htm

No. Blackberries are normally grown from established plants, or propagated through cuttings, suckers, and air layering. These articles will help with growing blackberry plants: https://www.gardeningknowhow.com/edible/fruits/blackberries/propagating-blackberries-cuttings.htm
https://www.gardeningknowhow.com/edible/fruits/blackberries/growing-blackberry-bushes.htm

It sounds like it may be rust. This article will help:
https://www.gardeningknowhow.com/plant-problems/disease/learn-about-plant-rust-disease-and-rust-treatment.htm

Sometimes newly planted plants do not make it through the winter. They are not as well established and do not have the reserves that mature plants do to help them through the cold weather. This article will help you figure out if the plant is still alive and you need to give it more time or if it has died:
https://www.gardeningknowhow.com/plant-problems/environmental/how-to-tell-if-a-plant-is-dead-and-how-to-recover-an-almost-dead-plant.htm

My guess would be that you may simply be picking them too early. Most people tend to pick blackberries when they are a nice glossy, dark color when in fact you should wait for them to dull in color before harvesting.