I am simulating a calm river with a lot of bends and the banks are not well defined, as in it is not well marked with depth on the sides. This makes the river splash above the banks wherever it bends and spreads out of the river's boundaries. Is there any way to define the banks properly while retaining small splashy movements near the banks and make the river make the turn and go according to the defined banks.

You may want to think about scale a little bit. Is your scene scaled to real world units? It does not have to be real world units but if you go too small those splashes may look a little unreal.

As far as escaping fluid, try creating a second collision object, I assume you already have one for the river bed, with higher walls. Then the escaping waves will have something to bounce off of. Also don't forget to play around with the Physical TAB of the collision and fluid object. Turn down bounce.

You can also get into vex velocity tricks to scale back velocity if it goes over a certain @P.y value. This assumes most of your river is fairly flat and waterfalls are not involved.