When walking, if I apply a force of 2N on the earth, the earth applies a force of 2N back on my feet due to Newtons 3rd Law of Motion. These 2 forces are equal in magnitude but opposite in direction, so they negate each other and add up to zero. So how can we move then if the net force adds up to zero?
In a sense your question is entirely apropos. The critical distinction to be made, however, is that the two forces can only be summed to zero if we are talking about the two-body system. Each body, considered in isolation, experiences an unbalanced force and thus experiences accelerated motion. The system, however, only experiences mutually-canceling internal forces. That is to say, a pair of equal and opposite forces internal to a system cannot cause an acceleration of the center of mass of that system. Ergo, even though the individual bodies are free to move without limit, the center of mass of the system will not move so long as a net external force is absent.