Manage mailbox labels — this allows DarwinMail to add and remove labels (inbox, snoozed, spam, etc) to your emails.
Manage your sensitive mail settings — this allows DarwinMail to update settings such as your forwarding address and aliases.
Manage you basic mail settings — this allows DarwinMail to update settings such as your signature and out of office reply.
View and modify but not delete your email — this allows DarwinMail to create your email (when you use the compose functionality), modify your email, and send your email (when you click the send button). This also allows you to update and save drafts.
Please feel free to check out the official documentation from Google for further reading.
Yes, DarwinMail is verified by Google.
What does that mean?..
DarwinMail basically sits on top of Google's servers and displays the data in the same manner (and in time using the exact same features + more) the same way as Google Inbox did.
Darwin does not store any of your email data whatsoever. In fact, if it did, Google would have asked me to audit the tool - but they instead granted me Google verification. It took them almost a month to break down DarwinMail and make sure it did not store any user email data.