Hey @Sky,
While there aren’t shortcodes within The Events Calendar or any of its add-ons at this time (except for some ones that basically replicate various Events widgets), the answer to your question about being able to customize templates on your site is yes.
Depending on your code knowledge / WordPress knowledge / creativity / etc., you can pretty much do anything you want on your site. We do not offer any help with custom coding here, or theme-related things, but we do have a very in-depth Knowledgebase article that shows how to make and customize various templates for The Events Calendar.
Check out this article here: https://theeventscalendar.com/knowledgebase/themers-guide/
If you want to just list events in a certain way, definitely check out the function tribe_get_events() – you can learn more about this function and see some examples of it here:
Using tribe_get_events
I hope this information helps! If you have any more specific followup questions or concerns let me know.
Cheers,
George