How and where are the canes on berry bushes and when to prune them?
These articles may help: https://www.gardeningknowhow.com/edible/fruits/raspberry/pruning-raspberry-bushes.htm
Once blackberries and raspberry plants have been trimmed for the fall, do we still need to water them?
Generally when the plants are done fruiting they will need less moisture.
Continue to make sure your watering if the soil conditions are dry. Do this until they are dormant.
I need to know when raspberry and blackberry plants go dormant in Central Texas.
They will go dormant at the end of the growing season in late fall and winter months.
My gooseberries and currants had a severe sawfly infestation that stripped just about every leaf. Fruit had already set and was too sour to be eaten. Bushes are alive and have started to sprout. Have pruned old wood and non-sprouting twigs. Should I feed now to encourage new growth?
I would treat with Neem Oil for the infestation.
Certainly trim away the damaged material.
Do not try to fertilize this time of summer.
Here are links that will help with growing and care requirements.
I am in the process of moving and dug my berry plants up and put the roots in plastic bags. Unfortunately, I didn't realize I should have put dirt in the bags as well. My daughter was supposed to water them but didn't. Now they are dried out. Is there any way I can try to revive them? thanks
No guarantees, but you can try some of the steps in this article: https://www.gardeningknowhow.com/plant-problems/environmental/learn-how-to-avoid-and-repair-transplant-shock-in-plants.htm
Learn more about caring for Raspberry plants here: https://www.gardeningknowhow.com/edible/fruits/raspberry/care-of-raspberry-plants.htm
Lately, I transported some plants from friend...now strawberry and blackberry leaves are turning brown and I wanna know the reason.
This looks to be either Strawberry Leaf Spot or Strawberry Leaf Blight.
Cultural practices are the recommendations to control these diseases.
In the image your soil looks quite wet, along with the leaves on your plants.
Well draining soil and keeping watering from splashing onto the leaves.
Crop rotation will also help in controlling these fungus diseases.
Here are some articles with more information.