If you are over quota, some services such as creating a new Google Doc may cease to function, however Gmail will continue to send and receive email normally.
In Gmail, when you attach something to an email, if that item is below 25 MB it stays in Gmail and applies to the Gmail portion of your overall usage. Larger attachments are saved in Google Drive and apply to the Drive portion of your overall usage. In both cases, the usage contributes to your overall quota.