Hi Marya,
Thanks for getting in touch and for your interest in our plugins. Events Calendar PRO does not include the ability for users to add events from the front end. However, our add-on Community Events does do that. You can choose to allow anonymous event submissions (with no login) but otherwise your users would log in via a form that looks like this: http://d.pr/i/j9wU (with a simple default theme). However, it will be pretty easy for people to figure out you are running WordPress.
You can decide if new events will be immediately published or set as drafts, and also set a notification email for each submission. You can read more about Community Events features on the product page and in the New User Primer.
Community Events can run with just our core free plugin, The Events Calendar. The Events Calendar has a simple Upcoming Events widget. Events Calendar PRO includes a more advanced version of that plus a mini calendar, featured venue, and countdown.
Let me know if I can answer any further questions.
Best,
Leah