I'm not sure I qualify as a newcomer anymore, but I'll make up for it with my enthusiasm for karma whoring :)
As Gayot Fow has already stated, the answers to your questions are:
To explain why, it boils down to the fact that as far as the EU and the international community is concerned, the "Turkish Republic of Northern Cyprus" (TRNC) does not exist and the Republic of Cyprus (ROC) has authority over the whole island. The Republic of Cyprus also believes this is true, and because EU citizens are allowed to travel freely in the entire territory of the ROC, they're also allowed to cross over to
the TRNC the Turkish-occupied bits of the ROC freely.
However, if you're not a EU citizen, things are more complicated. First, the ROC gets upset if you attempt to enter from the North, because in the ROC's view — and this is where we enter the bizarro-world of geopolitics — the border between the TRNC and the ROC is not really a border, and you've been in the ROC ever since you touched down at Ercan airport. So if you knock on the gate of the "actual ROC" at Nicosia, and they realize you entered the "theoretical" ROC without going through ROC authorities, you're now an illegal immigrant!
What about spending long periods of time in the TRNC without ever contacting the ROC then? If you're a European citizen, that's fine; but if you're not, you're an illegal immigrant as far as the ROC is concerned, at least in theory. Back in reality, though, they not only have no authority over you, but they don't even know you're there, and you'll only run into potential trouble if you're silly enough to enter ROC with TRNC stamps in your passport.
Other states in the EU, though, will share the likely opinion of my fair reader at this point: "My head hurts, make it go away." Which is why the Netherlands, or any EU country except maybe Greece, does not care about your TRNC stamps.
The only potential issue will be applying for the visa, as EU embassies in the ROC will likely require proof of ROC residence and embassies in Turkey will require proof of Turkish residence, and you won't have either. Neither will they accept any proof of residence issued by the TRNC authorities, because in their opinion the TRNC doesn't exist. So applying for the visa in your home country before you leave may be the easiest solution.