Would the Shinigami eye deal have shortened Light's lifespan? We know, that if a human makes the Shinigami eye deal, he will lose half of his remaining lifespan. But, let's say Light made the shinigami deal. He might have killed L earlier, thus prolonging his life again. So here is my questions:

Would Light have lived longer, if he would have had the Shinigami eyes?
Hypothetically speaking(since that is what it means to give Light the shinigami eyes at an early stage), if you give Light the shinigami eyes, the early he could have killed L, was when they were frequenting the same school/university and at that point L was already highly suspicious of Light to the point of tracking him.

If L were to die there regardless of how, it would trigger L's successors to come in with all the already collected information which again would be focused towards Light with the prediction of not to expose yourself to Light.

There is the fact pointed that Light could not kill without knowing one's name based on L's experiment, but would that be suffice for them to cease investigations at such an early stage which not even L ceased him self?