For problem 3:

1. you will want to verify that the integral (or wavelength interval
   weighted summation) of the filter response functions are unity.  I
   suggest you plot the response curves and view them before
   proceeding with your calculations.

2. the easiest way to make the computation for the magnitudes is to
   use a summation, rather than numerical integration.  You are
   welcome to do either.  If using a summation, you will need to have
   the stellar fluxes sampled at the wavelength points given for the
   filter response curves.  the easiest way to do this is to
   interpolate the fluxes of the stars, which are given at different
   wavelength intervals than are the filter response curves.  this is
   a common method.