- Yes, message body is searched.
- Try: "from:example.com OR to:example.com"
- No, Gmail UI and API search is not case-sensitive.
Be aware that service.users().threads().list() would be more consistent with Gmail UI search assuming the user has conversations enabled which is the Gmail UI default.
in:anywhere expands the search to Trash and Spam which is not normally included. Archived messages are normally included.