Can virtual particles be defined as the carriers of gauge boson forces?
Virtual particles need not be carriers of gauge boson forces for example, in photon-electron scattering the virtual particle is an electron. Virtual particles are simply those particles which are between two vertices in a Feynman diagram. Virtual particles are those which do not need to satisfy the dispersion relation - p2=m2.
The 'vpasolve' function is not giving any solution of the equation even though graphically I can see the existence of the solutions.
This is a common occurring as 'vpasolve' function tries solving the equation by numerically substituting the values of the variables and minimizing the error. From the graphs, you already know the range of the variables in which you can the solutions exist. Now if you provide 'vpasolve' these boundary conditions, it will definitely be able to get you the solution.
Can the magnetic properties of a magnet wear out with time? Can they be destroyed somehow?
Yes, magnetic properties of a magnet wear out with time thanks to earth's magnetic field. Simplest way to demagnetize a magnet is to heat it. The material becomes paramagnetic above the curie temperature and all the spins are randomized.