If a circular coil is placed in a time varying Magnetic field ,emf is induced but will there be induced current?
Yes, a changing magnetic flux will induce a current in a complete conducting loop. If there is a gap in the loop, then current cannot flow and the emf will appear as a voltage difference across the gap. Without a gap, the emf is dissipated by the current in the resistance of the loop and there will be no voltage difference between any two points in a circular loop in a symmetrical magnetic field.
Of course yes. Since you know about the Faraday's law, then you may know about the Lenz's law. It says that the polarity of the induced emf is such that the current produced by it, gives rise to magnetic field which opposes the external time varying magnetic field. The emf is the one that is "induced" and it drives the current and not the other way around.