Your Evernote account has an email address associated with it. If you forward the email to that address the entire email gets turned into a note, along with the header information attachments.
I've created a special contact with just my Evernote email. That way I can start typing "evernote" and it pops up as the first choice. You can also specify what notebook in Evernote the email ends up in. At @notebookname to the end of the subject line.
If you tap and hold on an attachment in Mail you should get either an Open In option, or a grid of compatible apps (depending on iOS version). Select the app that you want to copy the attachment too. Given the nature of DropBox, it is almost always a choice. If there are more than nine compatible apps, you may have more than one page of icons to chose from.
If a file is compatible with Pages (.pages or .doc), it will show up as well.
Pictures can only be saved to the camera roll, but you can then go into the DropBox app and upload them from there.
As you've notice, Copy only copies the link.
