Add checklist items to a step (1).  Leave all checkbox items non-required (2). Save a process.

Add "Update record" action to the step. Provide action name (3), choose execute "With Conditions" (4) and select "Formula" condition type (5). To get checkbox items values  choose "$Environment" Context Object (6) in "Merge Fields" settings. Expand "Context Object Items" picklist (7):

Create condition based on checklist options (8):

Due to above condition setting account will be updated only if ChecklistOption3 is checked.

Provide fields update settings (9):

Save the action. Start process and proceed to the step that has checklist items. Check list item (10) and click "Save" button (11). Proceed the step (12).

Account is updated with the new value (13):

Add checklist items to a step (see above). Save a process.

Add a rule to the connector that comes from the step with checklist items.

Add condition based on checklist items using $Environment Context Object.

Condition will prevent user from moving forward if none of the checkbox items were checked.

Save rule. Start process and proceed to the step that has checklist items. Do not check any item and proceed the step.

Rule is preventing user from proceeding the step as no checklist items were checked.

Checklist Items that are added to the step at the Process Builder, are available as "$Environment" Context Object properties (6); Checklist Items, added at the "Checklist" tab of Process Instance Progress component, surely, will not be shown in merge fields picker of Process Builder, but they are available to work with. To use them, do the following:

• See (in any merge field picker) what Checklist Option is last for the step (14). These are Checklist Options configured in Process Builder.
• Type "{$Environment.ChecklistOptionX}" merge field manually in the necessary place (or select any suggested in merge filed picker and amend number at the end of it's name to X), where X should be a number that is corresponding to the number of Checklist Option at the Progress component (15).

E.g., you have 3 checklist items configured at the step (17), but two more item was added in step Checklist tab (16). These two additional options will be available as "{$Environment.ChecklistOption4}" and "{$Environment.ChecklistOption5}" and you can pre-use them in email action (18):

These options values will be sent by email as far as others: