A portlet to display only shared To-Dos in Space is not available.
However, the uncompleted shared To-Dos assigned to you can be displayed in the scheduler for scheduling.
To display uncompleted shared To-Dos in the "Scheduler" portlet, on the "Scheduler" screen, select the Show uncompleted To-Dos checkbox in Options.
For details on the "Scheduler" screen, refer to how to view the scheduler screen.

You can display the uncompleted To-Dos assigned to you by selecting the Show uncompleted To-Dos checkbox in Options on the "Scheduler" screen.
For details on the "Scheduler" screen, refer to how to view the scheduler screen.

The space does not have user rights settings for restricting viewing, writing, and so on.
However, you can set the public and private spaces of the space to restrict access to users other than the participating members.
For details, refer to Creating Spaces.