SharePoint Online - Calendar - benefits and use?

I am working on incorporating a Calendar web part into my Sharepoint Online (O365) Team Site.
However, people's mailboxes aren't in Exchange Online, and I'm not sure exactly how the Calendar web part is supposed to be useful.

If I have multiple Calendars across various Team Sites, how would a use be able to see those from their primary dashboard of Calendar viewing, which is Outlook 2013?

If not, then is there at least a way to make new events put on the calendar automatically send invites to the users so they can accept and keep a copy on their Outlook? And receive cancellations upon those events being deleted as well?
garryshapeAsked:
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Adam BrownSr Solutions ArchitectCommented:
https://support.office.com/en-us/article/View-and-update-a-SharePoint-calendar-6bf4e154-f907-4453-b694-3191e8b1a963 has instructions for adding SharePoint calendars to Outlook. This doesn't rely on Exchange. It links Outlook to the SharePoint calendar directly. Note that if your users have an On-Prem Exchange mailbox or no Exchange mailbox, they would likely be prompted to enter credentials upon opening Outlook, so be aware of that.
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Ramkisan JagtapLead DeveloperCommented:
Individual users can visit the calendar and connect to there outlook using following steps:

1. In browser, open the calendar that you want to add to the outlook on the SharePoint site.
2. On ribbons Calendar tab, in the Actions group, click Connect to Outlook.
3. There will be a prompt to confirm that you want to allow the website to open a program on your computer, click Allow.
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