I have crabapple, cherry, and mulberry trees. When is the best time to cut off low-hanging, big branches? Also, can I straighten an established tree?

Prune your crabapple in fall to early spring. This is the dormancy period when major limb removal causes the least bleeding. Mulberries are also mid-winter prune candidates. Even in full dormancy, older trees may still bleed profusely. Cherries, either sweet or sour varieties, should not be pruned in winter. They are susceptible to silver-leaf disease. Pruning must be delayed until bud-burst in spring. However, if a branch is dead, diseased or damaged, it should be removed as soon as you notice it. This holds true for the crabs and mulberry as well. If you are merely pruning for convenience or aesthetics, wait until the appropriate time.

As for straightening an established tree, you need to determine why it is crooked. Are there prevailing winds, which have caused the trunk to lean? Was it improperly staked as a sapling? Is it seeking sunlight from under the canopy of an overshadowing tree? You can open up the canopy of an adjacent tree if shade is the cause. You can also prune the canopy of your leaning tree so that it appears more in proportion to itself. There are methods for forcing branches to grow in another direction. I would consult a professional arborist before attempting this on your own.