But when I loose that end there shouldn't be any restoring force(because I no longer exert any force) in the spring and the spring should remain in such an elongated state. But reality differs . Why?
You can imagine a spring as a chain (collection) of particles. First particle in the chain pushes the second, the second pushes the third and so on.. You are pushing the last particle in the chain, and the same particle is pushing you back (action-reaction). Once you stop pushing, the last particle also stops pushing you back, but is still being pushed by other particles in the chain until spring restores to its original position.
if restoring force and external force are action reaction pair then they are equal in magnitude.
restoring force being -kx depends on x which is a variable.
Correct and correct.
But common sense says it's easily possible to exert constant force.
Of course it is possible to exert a constant force. For a spring to compress, there must be two external forces acting on the spring - one from the left and one from the right. If one of these two forces is larger than the other, the spring will compress but it will also move (accelerate) in the direction of the larger force.
If one end of the spring is attached to a fixed wall and you apply some force while spring is relaxed, the wall will (almost) immediately apply the same force to the other end. The pushback that you feel from the spring at $\Delta x = 0$ is not restoring force by the spring but the normal force by the wall propagated through the spring.