The machine is a Baby Lock Tiara.
That's a rebadged Handi Quilter Sweet 16. It *might* be compatible with a Handi Quilter Little Foot hoop frame or a Studio frame (or whatever Baby Lock's name for those frames are), but you'd have to determine the revision number of the head. If it has a stitch regular or if you know for sure that it's compatible with one (I think they were called "Tru Stitch" and are a mouse/puck-like device) that would be a promising sign.