Some mailers include an X-Originating-IP header, allowing a recipient to see the sender's IP address trivially. Gmail does not include that particular header. The headers it does include will simply lead back into the Google network.
No, not X-Originating. Prosecutor asks to Microsoft to give all the details of xxx@hotmail.com. Microsoft sends all the informations of xxx@hotmail.com to the prosecutor. Google does not reply even.
I don't know what you mean by 'reveal IP addresses', but I can assure you that your latter statement is very much not the case.