Do the extraterrestrials experience premonitions? Or because that is a divine attribute, and they are nearly cut off, do they have to rely almost completely on time travel for knowledge of the future?

Extraterrestrials, curiously enough, do not have premonitions and it is for the reasons you state, that it is a divine level of intuitive sensing that is involved. This they have sacrificed through their own inner corruption through the millennia they have been infested with spirit meddler attachments dragging them down, introducing them to evil, and corrupting them from within to engage in all kinds of depravity. This has taken quite a toll and reduced their capabilities considerably. They are highly telepathic, but that is not the same thing as seeing the future. They are sensing what is happening in the moment and can read minds, for example, but they are not blessed with greater sensing beyond this in the same way as the human being. So they are more literal, and in lacking a higher awareness are quite vulnerable to corruption as well because they lack a conscience and are functioning psychopaths, totally loveless, and quite selfish beings. This, too, is a logical consequence of disconnection from the higher realm, that they are cut off from their own soul and their higher self, and especially from Creator, and will not be able to sense their soul purpose and tune into higher meaning about things in general. So despite having high intelligence and intellectual capability, they are literal-minded and materialist oriented and this is very, very limiting.