Ive been trapped by caravans on a narrow road.  Couldn't move in any direction because of ocean on both sides and caravans on the other sides belonging to my allies. 

Yes.  If you can get around it by selecting one unit out of your army and then moving it through the caravan, and then moving the rest of your army through the caravan to link up with the first unit (and you can, I've done it), it's kind of silly to block the whole army from moving through.

I've noticed that sometimes an army will go through a city, and sometimes it will go around it.  I wonder if that movement has the same problems as the caravan.

The game should not require space on intermediate squares or cities if there are enough movement points left and they are not stopping on the square, unit or in the city.