How to download submissions data?

Also, is there any way we can download the saved data up until this point (like a PDF or something similar) before I delete it?

Yes, you may download your submissions as Excel, CSV or PDF, you only need to follow this guide to achieve it: http://www.jotform.com/help/73-How-to-Partially-Download-Form-Submissions-as-Excel-CSV-PDF. 

Hope this helps.