Hard to comment without knowing more about the situation. But the Grandparents are usually the first ones considered for custody if the Mother can't have the child. When you say ''will they let him stay with me?'' Do you mean to have custody or to be designated a 'safe' adult he can go to if the Grandparents can't look after him at any time?
You certainly can apply for regular visits by the child to your house.
The SS will have assessed not only you, but also your house to see if it is safe for a small child.
For example,the father of one of my Grandchildren wanted the child to be able to stay with him at his house. The SS decided the house was not safe as it had a garden with very steep concrete steps that she could have fallen down the windows were also too easy to open meaning the child could get out without him noticing. He had to have a gate fitted so that the child could not fall down the steps and window locks.
I really don't like to criticize, but it is hard to be certain I am understanding the exact story as you have not written in sentences,no full stops or capital letters and just one comma in your question and replies.
Can you try to explain more clearly please it really will help understand a difficult / complicated situation.