It is possible to search for files via Global Search. Global Search will only return files that were uploaded via 24Files, i.e. Global Search will not search across all files stored in your SharePoint.
In case multiple files match the search criteria, these will all be displayed in the search results.
Salesforce allows you to customize the search layout of the object, see e.g. here.
Select the Search Layout for the 24Files Chatter File Link object and choose the fields that you want to display.