Copied checkbox also checked along with the original

Checkboxes with the same name act as the same field so if one is checked the other one will be checked too, unless you give them different export values in which case they will act as a group (like radio buttons).

If you need individual checkboxes, you will have to rename them.

There is no need to use copy/paste, when you create a checkbox with style you want, right-click on it and select 'Use current properties as new defaults' now every new checkbox will look the same, or you can simply right-click on a checkbox and select 'Create multiple copies'.