I just found that there is extension for mailchimp integration, but If I understand correctly, that extension is only for sync subscribers with mailchimp account, and I need to send newsletters from Mailchimp account.
My Question is,
if I point DKIM and SPF to mandrill records, can I use just Magento's extension to avoid spam blacklisting.
I mean, if I send newsletter from Magento admin panel, or Mailchimp account, and I have mailchimp's SPF and DKIM records, that is the same for blacklisting?
I'm not really sure what you mean with that. DKIM records are there to say that all e-mails sent by Mailchimp are authorized by domain owner (you). It's inteded to prevent forged sender addresses in e-mails.
You'll need to add SPF and DKIM records and verify ownership of your sending domains before you can send email through your account. Mandrill will not send any email from unverified domains or domains without valid SPF and DKIM records, including public domains like gmail.com, yahoo.com, and more.
A message that is rejected with the reject reason unsigned indicates that the sending domain hasn't been properly set up, and that your account is unable to send and authenticate email from that domain.
Refer to the documentation to learn more: https://mandrill.zendesk.com/hc/en-us/articles/205582267-About-SPF-and-DKIM
Just an input (from my side) - never use the integrated Magento newsletter, this is way to limited in functions and the interface is just not the same as "real" email clients, eg. Mailchimp, also there has been a lot of discussion over the year regarding the newsletter functions, and pros and cons using the build-in newsletter. Almost every response is pointing to use Magento as a collector of the e-mail addresses and the a 3. party for the actual newsletter handling/sending.
So sync you subscribes from magento to your email provider, and handle all newsletter functionality within eg your mailchimp account.