What is a FACT (and therefore can not be biased) is that the Turkish occupation of Cyprus is as illegal as it can get, the same goes for the pseudo state of "trnc".
The Cyprus problem as it exists today happened in 1974 when Turkey invaded and illegally occupied the north part of Cyprus. Of course problems in Cyprus existed before that, and the conflicts between Greeks and Turks in Cyprus started long long time ago like this:
Throughout the period of Venetian rule, Ottoman Turks raided and attacked at will. In 1489, the first year of Venetian control, Turks attacked the Karpas Peninsula, pillaging and taking captives to be sold into slavery. In 1539 the Turkish fleet attacked and destroyed Limassol. Fearing the ever-expanding Ottoman Empire, the Venetians had fortified Famagusta, Nicosia, and Kyrenia, but most other cities were easy prey.
In the summer of 1570, the Turks struck again, but this time with a full-scale invasion rather than a raid. About 60,000 troops, including cavalry and artillery, under the command of Lala Mustafa Pasha landed unopposed near Limassol on July 2, 1570, and laid siege to Nicosia. In an orgy of victory on the day that the city fell--September 9, 1570--20,000 Nicosians were put to death, and every church, public building, and palace was looted.
Thats how it started. The Turks came to Cyprus just to exploit us, and that is what they are doing since then. Cyprus had been under Turkish oppression for 307 years where Greek Cypriots were treated as third class citizens and butchered every time they demanded a bit of freedom.
In 1878 the Turks lost Cyprus to the British. But as you understand they wanted Cyprus back for strategic reasons. In the beginning the demanded from the UK to give them back the whole Cyprus, and when they realized this was not possible they started to demand partition of our island.
In 1974 they found the excuse they needed to put their plans into action and partition Cyprus. For the last 32 years years they illegaly occupy the north part of our country. So during the last 435 years, Turks have occupied Cyprus, and oppressed Greek Cypriots for the 339!! They started in the 15 century and they continue in the same barbaric middle age way even until today!
Greek Cypriots were butchered by them by the 1000s, and they still violate our human rights and refuse to give us back our land, and as an excuse they selectively use a time period of a decade to blame the GCs, forgetting all their crimes in Cyprus.
This is why in the Turkish propaganda you will always notice that they refer to a few very specific years, and even during those years they fail to mention their own crimes.
Basically lame excuses of the Turks that are trying to excuse even more crimes and illegalities against us, as they were doing for the most part of their history in Cyprus.
To answer some more of your questions:
What happened to make Turkey invade?
The reason was that they wanted Cyprus for their own strategic reasons, something admitted many times by the Turkish Generals who run Turkey. The excuse was the protection of the TC minority in Cyprus. Hitler has done the same when he invaded Czechoslovakia to supposedly protect the German minority there.
What are the facts?
Some undisputed facts are:
1) The occupation of Cyprus by Turkey is illegal
2) Their pseudo state in Cyprus called "trnc" is illegal
3) There is only one state in Cyprus, Republic of Cyprus, the north part of which is under Turkish occupation.
4) The Turks started the conflict in Cyprus, and they show no indication that they want to end it, since they feel they have the power to continue to exploit our lands and violate our human rights, as they did for the most part of their history in Cyprus.
Who are the Turkish people living there now?
Half are Turkish Cypriots, and the other half are Turkish Settlers brought from Turkey in order to change the demographics in Cyprus.
What made them want to occupy that area?
They want to occupy as much as they can, and they used their minority in Cyprus to do it, showing no respect to international law and the sovereignty of Republic of Cyprus. The reasons are the same as why Iraq had invaded Kuwait. (Strong big Nazi country VS small weak country near it) What differs are the excuses.
Also, this may be a stupid question...did the Cypriot people not kick off when they invaded? If so, why did no other country come to back them up like USA or UK - as we claim to be doing now, for example, when invading other countries and fighting for people's freedoms etc? I just don't get how it could happen.
The USA/UK intervene only were it suits them. For example they didn't bomb Israel when Israel had invaded Lebanon just a few months ago.
That said, the USA/UK along with the rest of world had convicted the invasion and had placed embargoes on Turkey for some years. But since Turkey was their good Allie they didn't want to spoil their relationship with them just for Cyprus.