I didn't know what a W5YI mystery antanna was, so I googled it and found this:http://vk1od.net/antenna/W5GI/
which answers your questions and then some...
Anything that has 'mystery" in its name implies to me that it's 'snake oil" anyway... and so seems to be the case here as well.
If I were you, I would reconsider the project. There is no magic bullet antenna that will be good on all bands.
Pehaps you have some bands that are more interest than others that you can focus on to find a good compromise design?
Some of the OCD designs are OK, but they have their limitations as well.
The balun choice depends on what the average impedance of the antenna models to be.