Yes, that's right.
> Then, why does applying the force on a longer portion of the lever create more torque?
Most of the answers to this question reduce, upon examination, to "that's how we define torque". We define the torque of 100 newtons at a lever distance of one meter as the product of 100 newtons and a meter, which we can call 100 newton-meters, which is equal to 1000 newtons at a lever distance of 0.1 meters.
But that doesn't really answer the question, which becomes, why is torque defined in this way an interesting thing to think about? And the answer is that if the lever is a rigid body free to rotate around a fulcrum, then 100 newtons at one meter in one direction will make it start to rotate, while 1000 newtons at 0.1 meters in the opposite direction will precisely cancel that "moment", as we call it, and there will be no tendency to start rotating. It's about what forces are needed to cancel each other.
Well, but, why should that be? Why does it take exactly 1000 newtons and not, say, 316.2 newtons? And I don't think I have a really good answer for that question. In the case of an elastic solid body it falls out of Hooke's law and the geometry of the situation, which you can reduce to two long, skinny triangles sharing a common side bisected by the fulcrum. But it seems to be much more general than that.
> I had thought it was because there is more mass acting on the point of rotation (longer lever = more mass).
Nope. You can try using a pair of scissors or a folding ladder as a lever, or pull in different directions on the end of a fixed-geometry lever. The lever's mass doesn't change, but the leverage certainly does.
