Good evening Lily and welcome to the Events Calendar forum!
Thank you for your interest in our products.
We’ll be glad to answer your questions.
It seemed the plugin generated a new page(or sort of) like http://domainname/event right?
Actually, it is not a “real” page, but acts like one.
The URLs for the full calendar view and the single events is determined by the value you input for both fields in Events -> Settings -> General
You can read about that here: https://theeventscalendar.com/knowledgebase/adding-a-calendar-link-to-your-site-menu/
So wondering if the entire calendar can show on home page as a wedge,not just a event list on side bar? If not as a wedge, is there any way I can make it work that way(with other widget)?
Absolutely. In order to be able to do that, you will need to grab a copy of our the Events Calendar Pro premium add-on: https://theeventscalendar.com/product/wordpress-events-calendar-pro/
Let me know if that helps.
Have a great day!
Geoff B.