Select the vertices you wish to separate and press the 'p' key.  This will separate that section of the curve into a new one.

If you reduce the Nudges parameter to 0, the vertices should be distributed in a Bezier fashion.

The Add-on works with Bezier curves.  Nurbs curves use different control points which do not interlock in the same way Bezier curve points do.

Yes, mostly: the corner vertices are created by averaging the two points on a corner.  If the curves a generally arranged in a 2x2 manner, the add-on may still create a mesh surface.

It is likely that the Fill operation does not have enough intermediate curves to define the surface well.  This can often happen with shapes that bend around 90 degrees. I would recommend dividing up the shape more and creating some intermediate curves that can add more definition to the shape you are looking to achieve.

Unfortunately Blender only allows you to make Operators not Modifiers.  Operators work in a one-time way.  I may experiment with making a modal operator, which might allow you to change the curves and have the mesh automatically update.  However when you click away from the mesh, the changes will still be permanently applied.

When creating a mesh from 1 or 2 curves, cyclic curves are supported.  For 4 curves, cyclic curves are not supported.

Try increasing the Samples parameter, which will increase the number of steps along the curve where the points are placed.  This can have an effect on performance but the vertices will be better distributed.

When the mesh is created from the curve, press tab to enter edit mode.  Then, select all the vertices by pressing a. Then, press space and search for Fill. Ensure that the Beauty checkbox is selected in the options tab.

This may be related to outstanding issue #1200 with Blender/Animation Nodes which is still being worked on.  

Current workarounds for large animations are to try rendering from the command line.  Make sure your work is regularly saved in case you encounter this bug.

The add-on creates a mesh using quad faces that would not fit well into a triangular layout.  If you wish to create a mesh this way, I would recommend you split one of the 3 curves into two. This will create a more uniform topology.