This is not my period so I’ll just sketch out what I know. The place we now call Northern Ireland didn’t exist back in 1600. The larger northern region was called Ulster stretching from Antrim to Donegal. In Raymond Gillespie’s words it was ‘a poor, sparsely populated peripheral region’. The population was about 200,000 (approximately 20% of that of Ireland as a whole). The economy was based on cattle. There were few large urban centres or markets.
Politically it was the most Gaelic part of the country with several dominant clans. This has been characterised as a social system of lordship over men rather than land. The clan owned land corporately and the chief received tribute income from subordinates. Women and landless men were firmly on the bottom of the social hierarchy.
The dominant political figure was Hugh O’Neill, who straddled the Gaelic and Anglicised worlds as The Great Ó Neill and the Earl of Tyrone. He successfully played both pro and anti English sides for years before openly rebelling in the 1590s. The defeat of the rebel Gaelic lords in the Nine years war which followed and their flight from Ireland in 1607 opened the way to the Plantation.
Sources
Steven Ellis, Ireland in the age of the Tudors 1447-1603 (Longman, 1998)
Liam Kennedy, Phillip Ollerenshaw (eds.), Ulster since 1600: politics, economy and society (Oxford, 2013)
It wasn't any different than the other Gaelic areas of Ireland, Northern Ireland didn't exist before 1921 but the kingdom of Ulster did, you can read about ancient and medieval Ireland here. http://en.wikipedia.org/wiki/Gaelic_Ireland
The English often documented that the Gaelic Irish were barbarians who needed to be civilized but non biased historians have proved that it was as much as civilized as any other region of Europe at the time, the Brehon Laws were the Irish laws of the time, historians often state how the laws were quite equal regarding sexes unlike many other areas of the world at the time. The Irish traded goods with other regions of Europe as far back as 2000 years ago, there was a skull of a gorilla found in Armagh from back then as an Irish king was given it as a gift from the Mediterranean. Most of the towns and cities of modern Northern Ireland still existed before the 1600's plantations, they were formed as Gaelic settlements or monastic settlements, e.g. Derry and Armagh, Armagh was the capital of Christianity in Ireland and still is to this day.
Ulster-Scots is a very simple term for plantation people, many of them were not from Scotland, many were from England. It must also be stated that were were many Scots in the north of Ireland before the plantations, from the 1200's to the 1500's many Gaelic Scots from the highlands and islands were recruited into the Irish clan armies and they were given lands in Ulster by the Irish clan leaders, many of these surnames are very common today such as McDonnell and McNeill. These Scots were very different to the Protestant "Ulster Scots", they were Catholic and very similar to the Irish culturally.
This topic should always be researched if you want to know about it because British people usually will say that the British were moved to Ireland in order to civilize the barbarians but this is really just unionist propaganda and is quite incorrect, you could argue that it was the Irish who civilized Britain, a good documentary to watch is "How the Celts saved Britain" https://www.youtube.com/watch?v=FxzM_Y0cYJA