Just what the topic title says.

The Bosmer are the more Stealthy based Mer society.

The Altmer are more magic oriented society.

The Dunmer are like a mix of the two but just way more xenophobic.

Don't forget their Orsimer (Heavy armored melee combat) cousins.

& the Maormer [It is possible "Maor"mer are loosely based on the ferocious Polynesian warrior people called the "Maor"i (that and maybe a bit of South American thrown in there as Beth tend to multi-influence from a general area) - but if so then they may be more Alteration based warriors like the Redguards as opposed to armor wearers]

No. The fact that there isn't a purely warrior based elven society doesn't automaticly mean that the Falmer were warrior based.

Really, no one can say for certain since we have next to nothing on them. Your really doing yourself a disservice by trying to categorize them like that though.

Orsimer are just as much mer as Dunmer are.

The Dunmer choice their faith the Orismer were forced into it. Anyway I wouldn't say the Falmer were warrior based. The only building we have seen from them used a lot of magic in it. So obviously they are capable of using magic as well.

Also, I don't really see why we would need one of each. We already have the Dunmer who are one of each on their own, and from what we see of the Thalmor there are a lot of Altmer warriors out there as well.

I don't quite get the need for such classifications. The very idea gives them a cultural stigma that isn't accurate in the least.