All users (including collaborators) on all account types can change tasks' statuses.
Use a task's status to clearly and easily communicate to teammates how a task is advancing and keep track of progress. By default, there are five task statuses that reflect the typical states in which a task can be in during its lifecycle. In addition to default statuses, Business and Enterprise accounts have custom statuses.
New: For (newly created) tasks you intend to work on but haven't started on yet. Tasks with a New status are displayed by default (when All active filter is enabled) in List view. You can adjust filters to see tasks with other statuses.
In Progress: For tasks you're currently working on. Tasks with this status are also displayed by default (when All active filter is enabled) in List view.
Completed: For tasks that have been completed.
On Hold: For tasks that are postponed. Tasks can be marked as On Hold even if they have scheduled start and due dates. Tasks marked as On Hold don't show up on the To-Do or Overdue widgets on your dashboard or on To-Do emails.
Canceled: For tasks that are no longer relevant or need to be completed.
Tasks can only have one status at a time.
From List view:
Navigate to the folder, project, or space where the task is located.
Right-click a task and hover over Mark as.
A menu appears with status options. Select a status from the list.
If you have custom statuses and want to select a status from a different workflow, you can hover over Change Workflow to see the list of other workflows. Hover over the selected workflow and select a status from the list that appears.
From Task view:
Open a task in Task view.
Click the task status in the task panel.
The list of available statuses appears. Select the status you need from there.
If you want to select a status from a different workflow, hover over All workflows to see the list of other workflows. Hover over the selected workflow and select a status from the list that appears.
Click the checkbox in the task's status field to mark the task as complete in one action. Note that if you're using fixed workflows and the status change is locked, you might not be able to do so (unless you're an account admin with the special permission enabled).
Yes, you can do that using mass actions in List view or from Table view using the mass edit feature.