Hi, Tim. Thanks for asking about the WooCommerce Tickets add-on functionality.
WooCommerce Tickets is basically an add-on facilitating integration between The Events Calendar and WooCommerce. As such, those issue regarding checkout may be better answered by WooCommmerce.
That said, WooCommerce does support discounts and customer registration. It may be a good idea to install WooCommerce (free) and play around with it so that you get a feel for what is possible.
Sorry I don’t have a more definitive answer for you. Please let me know if anything else comes up in your testing.