Why does the creature stay so long by the abandoned fire pit he found? Then why does he leave it? Why does he "lament" having to leave this fire behind?

I assume you are referring to Chapter 11 of "Frankenstein". The creature stays so long by the fire pit because he had never seen fire before, and it is a great relief to him to finally get warm. He examines the fire, finds out that it burns when touched, realizes that it is made of wood, and that the roots which he eats taste much better when roasted. He does his best to maintain the fire, but he has to leave it in search of food. Finally, when he leaves it, he "laments" because he doesn't know how to make fire again.