Can I save checklists as templates and reuse them?

Yes, you can save a checklist as a template and reuse it on other objects. To do this, open the popup dialog for an existing checklist (for example, by clicking on the name of the checklist), and then click "Save this checklist":

In the save dialog, select which objects the checklist is relevant for. This determines which objects the checklist can be added on.

You can also specify that the saved checklist should be added automatically to new objects in the project. For example, this way, you can create a Definition of Done checklist that is automatically added to all new backlog items created in that project.

After you've saved a checklist, you can add it manually on an object using the link "Or, add a saved checklist" at the bottom of the "Add a checklist" dialog:

If you don't see the "Or, add a saved checklist" link, there are no saved checklists in that project.