The dilution is as you described.
A very practical benefit of using it 1:1 is that you can average your developer and water temperatures to reach the final temp. If you developer is 60f and your want 70f, you can use some 80f water to dilute it to 1:1.
It's best to use it one-shot. You can get away with a second run if you give it an extra minute or so in the developer, but it's a last resort and reduces consistency. And consistency is something very important.