Shade will most likely play a big role in fruit production. Raspberries are usually planted in full sun, I believe that gooseberries are the same. Though, do you have a goosberry or a ground cherry?
Also with raspberries, pruning is huge for fruit production. Each year all of the old canes from the years growth should be pruned back to the ground and the new runners should be staked up to bear next years fruit.
And yes, you can transplant the plants. The best time to do this is the fall but, you can do it in the spring and summer. I put my raspberry plants in last June and was pleasantly surprised to see fruit on them. (Albeit, not that much but, that's the way the cookie crumbles)