Can we share Site anonymously?

We can give anonymous access in on-premise SharePoint Site/List/Library, but not in Office 365.
We can only share site/list items with external users in Office 365 but cannot allow anonymous access to a site.

Even with anonymous sharing access enabled for a site, when you share a site, the external users will be required to sign in with their work or school account (if their organization uses Microsoft 365) or a Microsoft account.

What are the corresponding SharePoint groups for the Draft Item Security section in Versioning Settings of a list or document library?

The security referred to by draft item security — Read, Edit, and Approve — maps to SharePoint’s Visitors, Members, and Approvers groups.