I have to be honest, and start this answer by saying that we can't answer most of these questions. Many archaeologists and historians would dearly love to be able to, and have been trying to for a very long time, but there's just so little data available. However, it is a subject that's frequently discussed, and there are a few things that can be guessed at or that we know outright.

As you already pointed out, many of the Greek terms that are used to refer to 'non-Greeks who lived in Greek territories at one time' are not used consistently. Pelasgoi in particular is used so widely and divergently that it's hard to really work out what they're actually identifying. But some of the terms you named are relatively stable and specific, and provide some sort of very incomplete picture of pre-Greek Greece.

Lemnians specifically refer to the inhabitants of Lemnos, an island of the northern Aegean Sea. We also know that a Tyrsenian language was spoken on the island, which is called Lemnian by modern scholars, well into 'historical' Greek times. But this information is very incomplete; we have no further direct evidence of native Tyrsenian speakers anywhere else in the Aegean at any point in the region's history. All other known Tyrsenian languages are solidly attested to Italy and the Alpine region. So lacking further data Lemnos' history of non-Greek speech becomes an intriguing and interesting anomaly that begs far more questions than it answers. The Greek's own tradition is that the island was settled by 'Sinties', which is a term that means 'raiders' but is also used by some authors as a term for an ethnic group. The Sinties as a people are referred to by different authors as Thrakians, Agriophones, and Pelasgoi, and give their name to the Sintike region of ancient Macedon. All we can say for sure is that the Greeks believed the Sinties to have been non-Greek speakers. Are these the same as the pirates referred to as Sinties, or were the two connected by folk etymology later on? Does the fact that the Lemnians were called Sinties mean that the wider Sinties all spoke Tyrsenian languages? These are questions we simply can't answer, as much as we'd love to.

Eteocypriot and Eteocretan both clearly refer to pre-Greek inhabitants of Cyprus and Crete respectively. Inscriptions in languages referred to by those names exist in both cases. On Cyprus a script descended from Linear A was used to write a pre-Greek language of the island, and on Crete the Greek alphabet was used occasionally to write inscriptions in a pre-Greek language of the island. In both cases we cannot fully comprehend the language, whilst being certain that neither are Indo-European languages, let alone related to Greek in any way. This is despite the fact that bilingual Greek-non Greek inscriptions exist for both languages. The corpus is just that small. It seems very clear that both islands had non-Greek native speakers during the historical period, and that the Greeks clearly understood there to be pre-Greek native peoples in the case of both islands. The temptation is to link the Eteocretans with the Minoan era culture of Crete, and the Eteocypriots with the pre-Greek culture of Cyprus. Both islands have Bronze Age written documents that have come down to us, the problem is that we still can't read any of them. We can't read the Minoan era Linear A script, or the parallel Cretan Hieroglyphs also used on the island. Neither can we read the Cypriot 'Cypro-Minoan' script. It may be that it turns out that the Eteocretans, and the Eteocretan language, are descendants of the Minoans era Cretans and the language of Linear A, but we simply cannot prove that true or false until Linear A at least is deciphered.

As for the Minoans themselves, that one is a bit complicated. The term is derived from the mythological King Minos, and was only applied to a civilization of people in the early 20th century. Arthur Evans was the first one to apply it to a historical, archaeological civilization of Crete's real history. This means that as a term it's an entirely modern one, with no ancient antecedent. At the time almost nothing was known about them, bar the references by some Greek historians to King Minos building a large sea Empire. So the term Minoan was swiftly used for an entire island and its inhabitants without really knowing anything about them, their language, whether they only spoke one language, their political divisions and cultural identities. This is why I've referred to Minoan-era Cretans, not 'Minoans', in earlier bits of my answer. We have a lot of useful archaeology that tells us a lot about Minoan-era Crete and the civilization that existed there. What we do not have is a lot of written context for it. Linear A is a script that seems to be native to Crete, and deciphering it is one of the great prizes of Bronze Age Greek history/archaeology. Until it is deciphered much of what we consider the 'Minoans' to be is a great big pile of guesswork, with all its literary context many centuries removed from the actual people in question. And, of course, how they relate to historical era 'Eteocretans' is just as based on guesswork too, for the time being.

As for what happened during historical times to all of these non-Greek speakers, we honestly can't say much for certain. King Evagoras of Salamis, a city of Crete, is known to have advocated replacing the Cypriot Syllabary, used for both Greek and Eteocypriot writings, with the regular Greek alphabet. But Eteocypriot inscriptions are already rare at this time, the late 5th/early 4th century BCE. It seems relatively straightforward to assume that after Greek speakers settled Cyprus, some time in the very late Bronze Age, the native speakers were slowly assimilated, and that this is likely the case for all the non-Greek languages. But the word 'assume' is a very bald one in that sentence, as it should be. We simply have no ability to prove directly what happened to these peoples, only the ability to say 'at this point they still had a distinct existence and at this point they no longer appear to do so'. We can attempt to use other ancient examples of cultural assimilation to project what might have happened but it's not proof. Just because the Anatolian languages were displaced by Greek in one way doesn't mean that this is how Eteocypriot was displaced on Cyprus.

To summarise, an awful lot of these subjects have almost no evidence to form conclusions from, and when it comes to the Bronze Age it's actually even more of an arcane mystery. We know that Mycenaean Greek, as we term the language represented by Linear B inscriptions, is not a direct ancestor to the Ionian or Dorian Greek languages, but it the only Greek language that is represented in the Bronze Age at all. As it was a language attached to a written bureaucracy we can't use the tablets as direct evidence of where the language was widely spoken, just as later use of Aramaic did not always mean that anyone outside of scribes spoke it in a given area. And somewhere, out there, the ancestors of most of the other historical Greek languages were being spoken. We can't even directly attest, in the Bronze Age, how much of Greece actually spoke Hellenic languages. We can identify the probable arrival of Greek speakers in the Middle Helladic era, we can read Linear B in the Late Helladic (aka the Mycenaean era), we know the general pattern of Hellenic languages and their speakers in the later historical era. That's about all we have to go on. Before archaeology was undertaken in the Aegean the picture was even more opaque. Before it was realised that Linear B represented a form of Greek, the general concensus had been that it would turn out to represent a Tyrsenian language, because that's what the legends and other literary snippets of the Classical era seemed to point towards.

However, as a final note, the pre-Greek speakers did leave their mark on Greece. Many Greek place names of antiquity, including Korinthos, Athenai, Zakynthos, Parnassos are all of non-Greek origin. It's believed some of them may have roots in the Anatolian languages, making them pre-Greek but solidly Indo-European, but several of them are seemingly non-Indo-European. This also applies to a sizeable body of general words in the Hellenic languages, which have no identifiable Indo-European etymology.