Hi Chris,
1) How do we know if something was done incorrectly in the database?
The best sign is that operations are progressing as normal.
You could definitely monitor your server’s error logs though for some extra assurance, and/or bring in a dev with particular experience in WooCommerce if you needed a manual audit of this.
2) I did remove the tickets from several events using the steps you gave, however, when I got back to the Event Summary for one of the events, the count is incorrect.
I suspect this may relate to an arguably unusual facet of WooCommerce, in that if product orders are deleted or manually added to the inventory count is not adjusted – if that’s so you would need to make the necessary adjustment manually through the product editor.
Does that help with this?