Violation of energy conservation in retarded interaction of magnet and coil If I move a magnet towards the coil then the magnet will experience a restive force because of Lenz's law. This way mechanical energy will convert into electrical energy.
But what if the magnet and the coil are a sufficiently large distance apart? The change in the magnetic field travels at the speed of light so the magnet will not feel any restive force instantly. Doesn't this violate the energy conservation law? Because we fix the magnet to a particular point before the restive force arrives at the magnet. And we will able to produce arbitrarily large energy in the coil.
If the magnet starts to move at time t=t1 and lets assume that t0 is the time taken for the flux linking the coil to change due to motion of the magnet.
t0 = (distance between the magnet and the coil/velocity of light)
the magnet will begin to experience resistance at time (t1+2t0).
so the delay will be 2t0.
In this time period (2t0), magnet is free without experiencing any resisting force. During this time period we can draw current arbitrarily large value by making arbitrarily large numbers of turns of the coil.
If energy is conserved, then what mechanism stops us to draw any large amount of power from the coil ?  
 A: The full problem involves an electromagnetic wave calculation. As you accelerate the magnet, the changing magnetic field launches an electromagnetic field and the magnet will indeed feel a force - the radiation resistance, very similar to the force opposing an accelerated charge. Likewise, as the wave passes through the coil, any field acting on the magnet propagates back as an electromagnetic wave. 
The magnetostatic calculation of this force is valid only for small separations, as you understand. In the small-separation limit, one can show that the electromagnetic waves travel back and forth very swiftly to set up the magnetostatic conditions that allow the approximate calculation. 
Any "time delayed" work through the effects that you note is accounted for as energy of propagating electromagnetic waves in transit. Energy conservation is upheld once one takes full account of the energy of the electromagnetic field.
A: If the magnet starts to move at time t=t1 and lets assume that t0 is the time taken for the flux linking the coil to change due to motion of the magnet.
t0 = (distance between the magnet and the coil/velocity of light)
the magnet will begin to experience resistance at time (t1+2t0).
so the delay will be 2t0.
In this time period (2t0), magnet is free without experiencing any resisting force. During this time period we can draw current arbitrarily large value by making arbitrarily large numbers of turns of the coil.
If energy is conserved, then what mechanism stops us to draw any large amount of power from the coil ?  
A: 
During this time period we can draw current arbitrarily large value by
  making arbitrarily large numbers of turns of the coil.

This is not a correct statement for the simple reason that the inductance $L$ of the coil goes as the square of the number of turns $N$ and thus, the time constant $\tau \equiv \frac{L}{R}$ increases with $N^2$.
Let $\Phi_{ext}$ be the externally generated (by a moving magnet or whatever) magnetic flux through the coil.  Assuming a resistive load of resistance $R$ is connected across the coil, the differential equation for the system is
$$L\frac{di}{dt} + Ri = N\frac{d\Phi_{ext}}{dt}$$
where $L = \mu_0\frac{A}{l}N^2$ and $A, l$ are the area and length of the coil.  Rewrite the equation as
$$\frac{di}{dt} + \frac{R}{L}Ri = \frac{N}{L}\frac{d\Phi_{ext}}{dt}$$
For simplicity, assume that the external flux is a ramp from zero over time $T$ so that
$$\frac{d\Phi_{ext}}{dt} = V_0\left[u(t) - u(t - T) \right]$$
where $u(t)$ is the unit step function.  It follows that
$$i(t) = \frac{NV_0}{R}\left[(1 - e^{-t/\tau})u(t) - (1 - e^{-(t-T)/\tau})u(t - T) \right]$$
where $\tau = \frac{L}{R} = \frac{\mu_0A}{l R}N^2$.

Now, For very large $N$, the current is approximately
$$i(t) = \frac{V_0}{N}\frac{l}{\mu_0A}\left[tu(t) - (t-T)u(t - T) \right]$$
and so
$$i_{max} = \frac{V_0}{N}\frac{l}{\mu_0A}T$$
which goes to zero as $N \rightarrow \infty$.  Thus, it is not the case that "we can draw current arbitrarily large value by making arbitrarily large numbers of turns of the coil"
