Trees need deep root watering. So during water restrictions, when you are allowed, give them a good long drink. And then mulch, mulch, mulch, to slow evaporation and keep the ground cool.
Minimize or stop pruning or trimming to avoid scorching your shrubs.
For best results, avoid planting until the fall. Local nurseries will often agree to keep your trees or shrubs until fall if you pay for them now when you have more of a choice.
Well, yes and no. It depends.
Are you purchasing a tree that is in a pot, or a tree whose roots are balled and burlapped?
If the tree is pot bound, wait until it drops its leaves in the fall, then fix the roots as described here.
If not pot-bound, container plants can be planted now. But if your plant is pot-bound and requires a lot of root system correction, it could suffer at least as badly as a freshly dug ball and burlapped tree.
It’s more about when they were dug than when they are planted. Trees can survive in the ground just as well (and probably much better) than just sitting around the nursery. The timing must be based on the condition of the tree more than the actual time of year.
Generally speaking, planting at a better time (between fall and early spring), would provide a less stressful situation for a tree. If you do plant now, choose a healthy non-pot-bound specimen and be sure to water and mulch properly.