Base movement distance is 1 BW for difficult terrain but there's a -1 BW for being in the river.  Does this mean they cannot cross OR for normal movement (where they are not being shot at or trying to evade) is there always a minimum of 1 BW the unit can move if the unit is allowed to move through that terrain type?

There is no minimum movement distance.  I would say that by implication the river becomes impassable.

As rivers are not used in competition battles, I would say you could make up your own rules for rivers on scenario games.  Personally I would allow a 1BW move in scenario games.

Thanks Richard, good to get the principle clear in my head at least. As you say for a scenario game we can then choose to ignore it in specific circumstances.