That message is misleading and we'll need to fix that. Using the home page as the base page just won't work. A WP Page needs to be created and set as the base page.
There should be (depending on your version) a System Alert that reads:
CiviCRM relies upon a base page in WordPress at http://example.org/, but it is missing. The default is https://example....
For your last question, a quick google of "civicrm mailchimp extension" gets
https://civicrm.org/extensions/mailchimp-civicrm-integration (usage 795)
https://civicrm.org/extensions/mailchimp-sync (usage 1)
If you install a drupal 7 tarball and mostly keep clicking next, and then install a civi tarball and mostly click next, it's the first set you've listed.
It is definitely not the 2nd one.
But to be fully absolute you need to include http:// or https://
For the bounce issue. See if you can find out if SPF and DKIM have been set up. See if you can send an email direct to your own contact. Does it arrive? Check the headers for SPF and DKIM results.
Look in Mail Account settings (under Admin > CiviMail), and check the account for the Bounces. It should show you the login so you should be able to login to ...