Right, we can't sync Fastmail contacts or groups. I understand there are apps that should be able to do that - look for CardDAV.
Now, what you'll want to end up with is an Contact Group in your Android Contacts. Can be synced by said "other" app, or created on the device, or created using Google Contacts on the web (and will sync to your phone).
Finally in Aqua on the compose screen - tap the "head" icon to the left of a recipient entry field, this brings up the app's own Contact Picker window which has a tab for Groups.
