Can I see how often my orders get refunded?

Yes. Go to Analytics → Reports and open Refund rate over time (in the Finances category, or search for it in Search reports…).

It counts orders whose status is Refunded, alongside cancelled orders, and shows the refund rate for each Week, Day or Month. You can also break it down by Country, Region, City, Sales channel or New or returning customer to spot where refunds come from.

Pick the date range at the top. Only orders you set to Refunded are counted, so keep order statuses up to date.