Is there a way to copy SharePoint 2010 list to SharePoint 2013
Including list items and workflows (SharePoint designer workflows)
No approval for third party migration tool.
I am afraid not. In order for a WF to be redeploy-able from SP 2010, they have to be attached to a content type and the CT has to exist in the farm it is moving too. Because it is a list workflow you will either have to use a tool (if one exists that does that) or recreate the WF from scratch in the new farm.