Suppose,I am pushing(or pulling) the door which is attached at one end,without bending my body.Then,I am experiencing a reaction force(from the surface over which I am standing) which is normal to the surface and along my body & which balances my weight.So,the force has no horizontal component,therefore no FRICTION.Then how can I push the door?

Though the components of force balance and therefore there is no transational acceleration of the door. But there is torque of the force about the hinge of the door which is not cancelled .This torque will provide the angular accelaration which will move the door.

The force that you apply on the door produces torque about the hinge of the door which causes it to move.The normal force that this action produes acts on the person opening the door by the door.This does not act on the door and produces no torque, So there is a net torque which produces the given motion of the door.