It will depend what day of the week it is.
A few years back, one was erected near where I live and the owners used to reverse the direction from one day to the next - presumably to even out the wear on the cogs/gears/bearings.
It does depend on which side you stand. The London Eye goes clockwise if you view it from the opposite side of the Thames, anti-clockwise if you view it from the South Bank.
If two people stand on opposite sides of a big wheel, it will APPEAR to be travelling in a different direction to each of them. In fact it WILL BE travelling in only one direction.
Exactly the same as two people standing on opposite riverbanks. To each of them the river seems to be flowing in a different direction - to the left or the right.
Not quite right - the river will seem to be flowing in the same direction - from the source to the mouth (presuming it's not tidal) - whichever side you stand. It's only when using ambiguous terms to describe it (as with the big wheel) that appearances seem to differ.