I found some site that explained collisions a little bit, and the formula from there is used here:
http://www.myphysicslab.com/collision.html
But it doesn't say anything about friction, and I don't completely understand it :(
Oh, and the blue ball is twice more massive then the red one, I forgot to say that in the description.

This is looking really great! The collisions seem to be working really well, and running the scenario for a long period of time doesn't seem to yield any problems :)
Just out of curiosity, have you seen my Rigid Body physics engine?

I created my own collision algorithm, but I have no idea how to implement rotation it it.
norm = norm.unit();
PhysicsObject a = this;
Vector2D ua = a.velocity;
Vector2D ub = b.velocity;
Vector2D uab = ua.subtract(ub);
if(uab.dotProduct(norm) < 0) {
double e = (a.elasticity + b.elasticity) / 2;
double f = Math.min(a.friction, b.friction);
Vector2D tang = norm.perpendicular();
Vector2D uaNorm = ua.projectOnto(norm);
Vector2D uaTang = ua.projectOnto(tang);
Vector2D ubNorm = ub.projectOnto(norm);
Vector2D ubTang = ub.projectOnto(tang);
Vector2D vaNorm = elasticCollision(uaNorm, a.mass, ubNorm, b.mass, e);
Vector2D vbNorm = elasticCollision(ubNorm, b.mass, uaNorm, a.mass, e);
Vector2D inelasticVTang = inelasticCollision(uaTang, a.mass, ubTang, b.mass);
Vector2D vaTang = inelasticVTang.scale(f).add(uaTang.scale(1-f));
Vector2D vbTang = inelasticVTang.scale(f).add(ubTang.scale(1-f));
a.velocity = vaNorm.add(vaTang);
b.velocity = vbNorm.add(vbTang);
}
I wonder if a solution would be to have a method that applies an impulse to a certain point on the body or something?

I think the impulse idea would work well. We know that since we are avoiding friction for the moment, a collision can only exert force along the normal. (And consequently with spheres, rotation does not occur) If we take into account friction, then there is a force tangential to the surface. Anyway, when you do impulse on a point, a percentage of that force goes into rotation, and the other percentage goes into translation.
This is a bit more difficult for me though, since I do my simulating in a completely different matter, by simulating the elasticity and deformation of the object XD

For the impulse function, I guess you can find the normal velocity component and apply that to the object's linear velocity. But for the tangential component, I am not sure how to calculate how much of it will go into rotation and how much will go into translation.

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