The transit method requires watching the light output of a star over long periods of time. A transit occurs when the planet crosses in front of its star from earths point of view. Since there is a small object (the planet) now blocking some of the star, it appears to dim a little bit for a while until the planet passes. If we are in a position where that occurs regularly (most paths of planets do not happen to be on the line of sight between earth and their star) we can deduce the period of orbit. From the amount of dimming and the period you can estimate the mass
Yes, our friend is right, because there is no contradiction to the law of conservation of mass in the above equation. It just the mass of the product is equal to the mass of reactants.. and that is shown in the equation you have presented earlier
