Thank you for contacting support. I’m sorry to share with you that the SharePoint 2013 is not supported. We already have logged an investigation to check the support of Aspose.BarCode with SharePoint 2013. I have logged this task under ticket id BARCODSHP-33148 in our issue tracking system. As soon as we made a significant progress, we would be more than happy to update you with the status of correction. We are sorry for this inconvenience.
Based on your second question, yes, you are right. Aspose.BarCode product is generating barcodes in the image file formats. There is no way to retrieve/download the barcode image from the list item. You can prepare a custom application to do so. Furthermore, Aspose.Pdf for SharePoint allows you to export lists, individual list item and Wiki pages in PDF format. http://www.aspose.com/docs/pages/viewpage.action?pageId=13304018
Please do let us know in case of further assistance or questions.