Was the Mycenaean civilization as unified politically as, say, Egypt at the same time? Was there one King of the Mycenaeans, or was the situation more like later Greece with independent city states?
The short answer is that current evidence suggests peer polities like Classical Greek poleis, or city-states. Virtually everything we know about the Mycenaean civilization comes from archaeology. While we can read their script, which is called Linear B, the entire corpus of their writing to survive is very bureaucratic in nature, and most texts are short term records of the palaces that were accidentally preserved when those palaces burned down. So these texts show detailed organization of a region controlled by its palace (the best example is Pylos controlling pretty much the entirety of Messena, which is no mean feat for an Archaic state). We are able to gleam a good amount of information about the state from these rare texts. For example we know the palace system was ruled by a king called a wanax. We know Mycenaeans worship many of the same gods later Greeks worshiped like Zeus, Hera, and Dionysus. We know that several of these gods had cults with estates of their own independent of the state which would interact with the local economy. But what we do not have is textual evidence for political relationships between these different states. There is evidence for trade, and interaction between regions of Greece ruled over different palaces. But no solid evidence for anything like a grand monarchy and central government that you might get in Egypt or with the Hittites. (cf. Shelmerdine, C. W. ed., The Cambridge Companion to the Aegean Bronze Age) edit typo