Principle of locality and forces I have a silly confusion about the statement written in the link   Einstein and Locality
''external influence on A has no direct influence on B; this is known as the Principle of Local Action.''
Since GTR and Electromagnetism obey principle of locality. And in both cases change in A position affect the B and vice versa. Then why this contradiction come.
Please correct me.
 A: EM and GR don't actually say that "particles exert forces on each other". What they actually say is that particles produce electromagnetic and gravitational fields, and that these fields then interact with other particles. Significantly these theories describe these fields using differential equations, which means that the field at some point in space is completely defined by the field in its immediate neighbourhood. If a charged or massive particle accelerates, this causes a change in the local field around the particle, which creates a disturbance that propagates outwards as the field reconfigures itself. This disturbance propagates at the speed of light (in fact in the EM case it is light) so there is no violation of locality. 
It is important to realise that the principle of locality requires that these fields are in some sense "physically real" (whatever that means) and are more than just a clever bit of maths. In the case of GR we have a nice picture of the field in terms of the bending of space time, while trying to understand what an EM field is leads to QFT.
A: I'm no expert in quantum mechaincs, but as @polyphant said, Einstein termed this phenomenon as "spooky action at a distance". In quantum mechanics, it is believed that there has to be a certain way in which quantum information(quantum bits) can travel from one place to another without moving the physical matter to which the information is attached. This phenomenon is called as "entanglement"-particles separated by light years can still appear 'connected' to other particles, with the state of one particle instanteneously(yes, speed of light is no longer the limiting speed) affecting the state of other. (most generally, while studying this topic, the information is spin states). Indeed, it is one of the contradictions between relativity and quantum mechanics. (personally, I believe relativity should win..:))
