I have two weigela bushes that are in the second spring/summer from first planting them. Should the light pruning after the spring blooming period be to cut back all the flowers, or cut some of them in order to give them a more defined shape?
This depends on how large your shrubs are and if you need to shape them.
If the size of the shrub is fine right now, just dead head the flowers.
If you need to shape up your plant them go ahead and make those pruning cuts after blooming.
https://www.gardeningknowhow.com/ornamental/flowers/jasmine/trimming-jasmine-plants.htm
Would like to move this shrub to another full sun area.
Here is an article with transplanting guidelines that will help you:
https://www.gardeningknowhow.com/ornamental/trees/tgen/transplanting-trees.htm
Can you take cutting off a mature plant to start a new one?
Absolutely! This article will walk you through how: https://www.gardeningknowhow.com/ornamental/vines/wisteria/propagating-wisteria-cuttings.htm
My weigela bush has white powdery substance on some of its branches. I am trimming my well-established weigela bushes after their spring bloom and I noticed this year that the backside of the bushes (next to my front porch) have a white powdery substance on some of the branches. What is it and what can I do to take care of it?
Your plant has Powdery Mildew. You can use Neem Oil to treat.
Here is a link with more information.
https://www.gardeningknowhow.com/plant-problems/disease/powdery-mildew-homemade-and-organic-remedies.htm
https://www.gardeningknowhow.com/plant-problems/pests/pesticides/neem-oil-uses.htm
The leaf tips on my Weigela tree are turning brown and drying up. Is it getting too much water or not enough? It is planted in a rock bed. Is it too hot for it? The soil is sandy.
Weigela need a rich moisture holding soil, and should be kept moist throughout the growing season.
The sandy soil is likely not holding enough moisture for your shrub.
Here is a link with more information.
https://www.gardeningknowhow.com/ornamental/shrubs/weigela/growing-weigela.htm
My plant is not blooming. It gets plenty of sun. It is a year old. Any suggestions?
I'm sorry your Weigela is not blooming! Plenty of sun is good, but make sure your soil is moist and well-draining, too.
Weigela blooms on last year's wood, so it's possible that even though your plant is one year old, it hasn't had a chance to mature enough to support new blooms yet. In other words, THIS year's wood may support new blooms next year.
These articles may help you:
https://www.gardeningknowhow.com/ornamental/shrubs/weigela/pruning-weigela.htm
https://www.gardeningknowhow.com/ornamental/shrubs/weigela/growing-weigela.htm
https://www.gardeningknowhow.com/ornamental/shrubs/weigela/growing-weigela.htm
It's a new plant. It's been in the ground about three weeks. One week after planting it accidentally got flooded with irrigation water so I didn't give it anymore water for a week. Then it was hot and dry and I suspect spider mites moved in. I bathed it with insecticidal soap and have been watering regularly. I live in central AZ, I think zone 8.
This plant will probably become more healthy as it settles in. These articles will help you:
https://www.gardeningknowhow.com/plant-problems/environmental/what-causes-brown-edges-on-leaves-of-plant.htm
https://www.gardeningknowhow.com/plant-problems/environmental/learn-how-to-avoid-and-repair-transplant-shock-in-plants.htm