Are you doing this in code (C#/VB)?
If so, I don't think you can send an email to a SharePoint Group, but you will be able to enumerate that group, get all the users' email address from it, and send an email to each in turn.
If you're doing this with a workflow, I'm not entirely certain - only way is to try and see what happens (create a SharePoint Designer workflow to test if you like, very simple test to a SharePoint Group that you create as a test with 2 users in it, for example, and create a task in the workflow that sends an email to that workflow).
As for sending attachments - not sure if SharePoint can do this out of the box, the idea being that attachments are a thing of the past and that documents, etc. are linked to in the email that's sent.