A checkbox set is merely a convenient way of entering data. The actual field contents is a return-separated list of the values checked—if only one value is checked, that will be the content, but if someone checks more than one value each will be listed in the order in which they were checked.
If you want to display the field contents in that way in your report, you only need to make a standard text instance of that field (i.e. without checkboxes) large enough to accommodate the list (with sliding set if needs be so as to show only what is there). If on the other hand you wanted to show the checkbox values on a single line, say comma separated, then you would have to create a report field that displays the values from the checkbox field with a substitute calculation to replace pilcrows with comma + space.
Study triggers. Try OnObjectModify or OnObjectEnter to detect the changes in the checkboxes, then you can do whatever you want in relation to its related record.
Related links you might find useful: