woocommerce cart page problems

I needed to restore my website from backup, but since then there are strange things going on with my shopping cart page. see link:

https://www.helpmij.nl/forum/attachment.php?attachmentid=240621&d=1436122535

Not only are the Basket totals mentioned twice, even the “Proceed to Checkout” button appears too often on this page.

Another problem : if I choose “free shipping”, the total amount is not adjusted (automatically, or not at all?), whereas previously this was working fine.

Any ideas?