We do not include “Products” as an option by default, as users were reporting some issues adding tickets to products in the past. Tickets are WooCommerce products themselves.
If you would like to add this option back in, you can do so using the snippet in this post. However, please note that we are not able to support customizations like this, so any issues that you may run into with adding tickets to products would be outside the scope of support that we can provide here in the forums.
Yes, Event Tickets and Event Tickets Plus do not require The Events Calendar to work, but that is where all the event management functionality comes from. It’s free, so I would definitely recommend installing it on a staging site to test it out!
I’d also recommend the following articles, which have a lot of good info on getting up and running with our plugins: