You may send any kind of attachment, as long as the resulting email is under 70MB in size (due to encoding issues this usually means an attachment of 50M). Attachments with names of the form 'filename.doc.exe' are commonly used for virus transmission, because under Windows they are shown as 'filename.doc' (hiding the fact that it is an executable program); these types of attachments are blocked for this reason.
FastMail does not carry mailing lists used to distribute binaries (e. g. images, MP3s, etc.) for guest accounts. Messages to or from these lists will be rejected. Paid accounts do not have this limitation.
There are per-hour and per-day limits on the number and size of emails you can send and receieve dependent on your service level. These are detailed on the pricing details page.