It's very hard to determine what the "general public" knew about anything during the Middle Ages, as your average peasant was not literate and thus did not leave us records of their beliefs and knowledge. The average educated person would have been aware of the empires in the past, especially Rome and especially in Germany which was actively claiming to be the successor state to the Roman Empire. They also would have had access to various chronicles, histories, and the like which detailed more local history, though how likely they were to have actually read these is a more difficult question to answer. It likely varied quite a bit depending on who/where/when we're talking about.

On technology and culture, I think it's safe to say that they had less of a grasp. More, to my eyes, because they simply didn't think about history in those terms. If you read medieval histories they spend essentially no time on the subject of technology and the culture of the present day (i.e. when the texts were written) tends to get projected back into whatever past they're talking about, so you have knights in ancient Israel, Alexander the Great being a sort of proto-Christian, and so on.

They definitely anticipated change in the future, but not cultural and technological change. What they expected was the rise of the Antichrist, the great persecutions of the faithful that would follow, his eventual defeat, and the triumph of Christ before the inauguration of the new heaven and earth promised by Christian eschatology.