TO stop sending spam email from mail:
In order to re-secure an account that has been compromised/hacked/stolen you will need to check and fix at least all of the following settings.
But first you need to check the bottom of the Inbox and make sure your account is not open at any other locations. If it shows additional locations, open the Details window and "Sign out all other sessions".
Settings -> Accounts and Import -> Google Account Settings -> Change Password [pick a new secure password]
Settings -> Accounts and Import -> Google Account Settings -> Change Password Recovery Options [verify secret question, SMS and recovery e-mail address]
Settings -> General -> Signature [make sure nothing as been added]
Settings -> General -> Vacation Responder [make sure it's disabled and empty]
Settings -> Accounts and Import -> Send Mail As [make sure it is using your correct e-mail address]
Settings -> Filters [no filters that forward or delete e-mail]
Settings -> Forwarding and POP/IMAP -> Forwarding [disabled or correct address]
Settings -> Forwarding and POP/IMAP -> POP Download [disabled]
Settings -> Forwarding and POP/IMAP -> IMAP Access [disabled]