Assuming we have a very powerful telescope, and a huge mirror 1000 light years away from earth, is it possible to look at this mirror to see what people did on earth 2000 years ago?
Is it even possible to build such telescope, are there anything discovered in the universe that can act like a mirror?
There is no object that we currently know of as a "mirror" pointing at Earth, nor is there much chance that such an object could exist (everything solid that reflects is typically either tiny or surrounded by too much diffuse material, and gravitational lensing can't bend enough light back around to produce a decent spatially-extended image).
That said, suppose such an object did exist. How big would the telescope have to be to be able to see a person from 2000 years ago?
The key number to look at here would be the angular diameter of a person from 2000 light-years away. Given that the average person is around 1.8 m tall, and 2000 light-years works out to $1.9\times 10^{19}$ m, this gives us an angular diameter of
$$\theta = \frac{1.8}{1.9\times 10^{19}}=9.5\times 10^{-20}\textrm{ radians}$$
The reason this is important is because angular resolution in a telescope is limited by diffraction. Due to diffraction through the aperture of the telescope, even sources of light that are infinitely small will be seen to have a certain angular diameter. This diameter is essentially the distance at which two separate points of light become indistinguishable. In order to have any hope of looking at a person, we have to be able to distinguish them from the other things around them; as such, we must have an angular resolution of at least $9.5\times 10^{-20}$ radians. The angular resolution of a telescope is determined by the aperture diameter $D$ and the wavelength of the light $\lambda$ by the Rayleigh criterion:
$$\sin\theta = 1.22\frac{\lambda}{D}$$
Plugging in $\theta=9.5\times 10^{-20}$ and $\lambda=500$ nm (since we want to see visible light) yields:
$$D=6.42\times 10^{12}\textrm{ m}\approx 43\textrm{ AU}$$
which is roughly the distance from the Sun to Pluto, on average. So we would have to build a telescope that stretches from the Sun to Pluto to even have a chance to overcome the diffraction limit (and that's under perfect conditions, so this is a lower limit on the size).
