Cyprus was obviously a huge mining center for copper in the early and middle bronze ages. It was called Alashiya, but which culture was dominant there? Minoan? Pelasgian? Philistine? Phoenician? Canaanites? One webpage i read said the people came from Anatolia, which is very vague, does that mean Hatti? Hittites? Hurrians? Or were they an independent culture? Did they have a King? What language were they speaking at that time?
They appear to have been relatively independent, isolated, and not terrible cohesive. MCI contact with other cultures was sporadic, with little to no contact with either the Egyptian or Levantine cultures. This changes around 2300BC, and really picks up by about 1650BC (MCII-III periods) where lots of exchange with neighbouring countries takes place, but there appears to be no overall 'control' and they appear to have no king - mostly tribes - and the fortifications seem to show this. It's the LBA/LCIII period when the Greeks start arriving (circa 1200BC) where it becomes more Greek. Part of the problem is that there is a lot of material continuity up until the LCIII period, which means it's difficult to track any major changes in population composition.
It was called Alashiya,
Although the Mari texts suggest this, it is a disputable point (just fyi).
There is no evidence for writing (so far) so language is a bit difficult to ascertain. Most scholars agree that it's southwestern Anatolia or possibly Cilicia which are the sources for innovation in Cyprus, but whether this also means language isn't sure.