Any suggestions how to display existing list in chart, or graph. Chart Web part is deprecated for 2013.
Also 3rd parties aren't an option?
Use jqplot for the same. You can get from Google.
You could use CSOM to read the data from lists and Chart.js to create the graphs.
Sample: http://www.c-sharpcorner.com/blogs/create-a-chart-using-chartjs-in-sharepoint-server-2013
.webpart
file from the web part galley in SharePoint 2010 and upload it to your site collection web part gallery in SharePoint 2013. And after that you can use chart web part in SharePoint 2013 as well.