This might be a silly question but if light travels at the speed of light and time is frozen in that speed then why the stars we see could be dead already and not just instantly disappearing from the sky the moment it explodes/dies?
Because we are not moving at the speed of light.
From our point of view, light travels at the speed of light, and so events on a distant star are not visible until the light reaches us.
From the point of view of the photon, the universe is 2 dimensional (it is flattened by infinite Lorentz contraction) and there is no passing of time (infinite time dialation). The star and you are at the same point. Photons have a weird point of view.
Fortunately we don't have to worry about that, because we have mass and so we are not moving at the speeed of light. We have a 3d universe and we have a dimension of time. Thank Higgs we have mass!
It is the same reason for why we see the Moon. If the moon exploded, we would see the entire thing happen. Objects in space don't 'instantly' disappear and even when far away, light always gets sent in the same order and we see what happened.