I want to create friendly tasks reminders at the beginning and end of every week that are visible to everyone in my team.
Yes and No.
You can create a task within a shared project, which all your team members are added too. They will be able to see this task. Though, only one person can be assigned to a task at a time. So you'd have to leave it unassigned for everyone to view it.
Would be so great to implement the feature to assign a task to multiple team members!