How does the width or depth of a container of water affects the speed of an object (e.g. a toy boat) travelling on it?

Try thinking along these lines:

When the object moves forwards, water has to move backwards, to make a new "hole in the water" to be occupied by the object, and to fill up the "hole" where it was before.

If there is only a narrow space between the object and the walls, the water has to move backwards faster than the object is moving forwards.

You might want to try googling for "virtual mass" in fluid flow, which is another way of thinking about the same effect.

Look up laminar flow and notice that resistance increases with velocity gradient (difference in velocity over separation). The further away the walls the lower the velocity gradient (the higher the separation).