Can I change or move every planting of a succession at once?

Yes, and it saves you editing five plantings one by one. Right-click any planting of the succession and choose Edit Plantation Group to change them all; Heirloom warns you that this can override what you changed on a single planting.

To shift the whole succession earlier or later, right-click one of its plantings, choose Select all group to drag, then drag. To change one planting only, click its bar and edit that planting.

The steps are in Plan a succession.