When you sign up with Outlook 365 you get allocated a sub-domain like contoso.onmicrosoft.com. If you send an email from user@contoso.onmicrosoft.com should it not automatically be signed with DKIM or do you need to do anything extra?
Emails are not being signed with DKIM and also the reverse DNS check is failing, whereas I would have expected both of these to work as standard.
DKIM should be enabled by default with your .onmicrosoft domain. There is nothing to do as far as the .onmicrosoft domain is concerned. I would put in a support request if you are not seeing your outgoing messages signed.
As for reverse DNS, that seems to work fine. I tried multiple IP's resolved from lookup and each one resolves back to the Microsoft servers. I'm not sure where you are testing from, but you may want to validate from a few a few different places and make sure it's not a local device causing your issue. If you have some sort of edge device modifying message headers before it reaches you, that could be the issue in both cases.
