I think it goes about 6mph. I agree with your maths though, so probably my estimate of the gear ratio is wrong.

I don't know how long the battery lasts, we have never driven it for long enough to flatten the battery.

While I was building it I used it for about an hour doing several laps of dragging a "trailer" full of rubble from the top of the garden to the bottom (the easy direction - empty load on the way back up) and it became noticeably slower towards the end but still got me up the hill. So I'd say it lasts over an hour.