I think it is better to assume that monomolecular is just sci-fi speak for very thin very strong rather than literally one molecule. Once you get to the molecular level the physics just start to work differently. You have to think about the strength of the bonds between molecules and the bond between atoms in those molecules. The best analogy I can think of is imagine trying to use a chain of magnets to cut apart a ball of magnets. And to put it into scale the ball you are cutting through has to be the size of a house. Your chain of magnets (or molecules) has to be held together more strongly than whatever you are cutting and that is just one of the problems.
But even ignoring the monomolecular bit you still run into problems with the idea of a web spinner. Anything spread out that much would create huge amounts of drag. Yes, you can overcome this by weighting the edges but then you have to propel the weights with enough force to overcome the web parachute slowing them down. It is more practical to just project the weights at a higher speed without the web and count on them to do the damage.
While a lethal web gun sounds cool in real world application it is going to be limited to short range non-lethal.