Yes, others on your team can view your tasks. However, only Admins and Organizers can edit tasks belonging to another team member. Someone with the Team Member role can only edit tasks that belong to them.

Note: You can see other team member's tasks, but only yours will appear in your task list that drops down from next to your profile name.

To assign a task to another team member, simply click on the down arrow next to the name under Owner.

This will then pull up a list of team members that can be assigned to that task. When creating a new task, or duplicating an existing task, it will be assigned to you by default but can be changed at any time. Once you assign a task to another team member, it will appear in their task list.