How infinite Nash equilibria are possible in a game?
Well the intuition is quite straightforward: as you have mentioned yourself, player 2 is indifferent between playing any action in pure strategies, or randomizing in any possible way. So, for a mixed strategy equilibrium to exist, player 2 needs to play L w/ probability 4/7. If this is the case, it is irrelevant what Player 1 player---player 2's outcome is the same. As a result, in pure strategies the Equilibria are L,L and R,R and, in Mixed strategies, q=4/7 and p can take any value between 0 and 1. Hence, there exist infinite possible Nash Equilibria (p just has to obey the fundamental laws of probability).