The EPR paradox was resolved a while ago, strongly in favour of Einstein's "spooky action at a distance". The first experiments were done in the 70's. See:
Yes, but as with most things in physics, the first signs that an idea is dead usually come decades before the ghost is truly given up. Take, for example, this work from 2012 that was still dealing with a variation on the "hidden variables" formulation: http://arstechnica.com/science/2012/10/quantum-entanglement-...
A theory is (as Heisenberg explained in his book "Physics and Philosophy") an interpretation of data based upon unscientific, non-falsifiable, a priori assumptions on the part of the theorist. You can't really disprove something as nebulous as "hidden variables." That's not a falsifiable statement. What you can do is disprove some theory based on hidden variables. Such evidence does not apply to the possibility of other theories of hidden variables that are yet unformulated.