Beth, the hand punch that's pictured is a knock-off of a Roper
Whitney portable hand punch. I own both sizes of the Ropers and have
also tried the knock-offs owned by others. (There is no comparison,
by the way!) The smaller hand punch set comes with seven dies. I also
own all of the additional sizes of Roper "bits".
You can purchase the Roper and all of the bit sizes individually in
1/64" increments from MSC Industrial Supply Co. However, I don't
think the Roper punch bits actually work in the knock-off versions
because of the patented way they're inserted which reduces the force
needed to punch the holes.
I also have never seen shapes other than round for the Roper
punches, but they may exist. MSC's customer service is very good and
if you call them they'll find out for you.
The Roper Whitney is more expensive, but if you can afford the
upgrade I highly recommend their punches. I've had mine for 13 years,
have punched thousands of holes in all gauges, and the bits are still
sharp. It's a tool that's worth every cent.