It appears that the float on your sump pump is not set right. It is coming on as soon as it senses water as opposed to waiting until there is a decent amount of water in the sump. iI believe if you simply move the float ball up a little the sump will come on and stay on for a longer period.
As for the sump outlet. As long as the water is going away from the house it would be fine (grading of the land). It doesn't sound attractive to have the pipes the way they are and you might want to have the contractor fix it.