One interesting thing about escape velocity with Gravity in 2d is that it does not depend on the distance from the center of mass of an object. If you were 1,000,000km away from a planet that had a radius of 5,000km the escape velocity would be the same as if you were on the surface. The equation for escape velocity in 3d is sqrt(2GM/r) but in 2d the escape velocity would just be (2GM) so that it doesn't have any dependent on the radius.
Also a mass in 2d would either have no schwarzschild radius or any finite radius would be within its schwarzschild radius so a mass would either be too small to be a black hole or would be a black hole that would take up all of space. In a 2d universe there would either be no black holes or the entire 2d universe would be in a black hole. In 2d if a mass was to satisfy the equation sqrt(2GM)>c then it would be a black hole regardless of density or radius and if it was to satisfy the equation sqrt(2GM)<c then it could never be a black hole regardless of how small its radius was and regardless of how dense it was.
Also because Gravitational Potential Energy is equal to Radius times Force the Gravitational Potential Energy between two masses in 2d would not depend on the distance between them.