Hey Robert,
You can indeed customize the submission form – and lots of front-facing parts of the plugin – by following the guidelines in our official Themer’s Guide here → https://theeventscalendar.com/knowledgebase/themers-guide/
As for showing the user ID, this is something you’ll have to play around with, but it indeed may be possible with some core WordPress functions like get_current_user_id() or, more likely, by querying for the author of the submitted event and getting that ID.
While we can’t help with specifics of coding or implementing customizations, hopefully the information here is a helpful first start.
Cheers!
George