I can receive my new Facebook eMails in GMail, but is there a way to answer these messages from GMail?
I’m talking about the emails in the inbox, not the status.
Yes you can.
Just found this unanswered old question from similar questions:
You just have to click on reply type and send.
You can post comments and reply to messages by replying comment and message notifications.
I don't think there is a way to do that simply because Facebook doesn't support that functionality. And I really doubt they will offer that feature in the future as not letting users reply to messages from within email drives traffic for them.
After researching a bit, I don't think Facebook has come out with this feature. It seems as if they allow posting replies to comments that they would allow the same for messages but who am I to judge?