Proper baby mouse care?

We recently found a whole litter of baby mice with the mom in an outdoor vacuum so we put them in a safe spot and when i went to see if they were there, there was only two baby mice, one dead and one alive. I took the alive one and put it in an old hamster cage that i have... (I will assure you that i cleaned the cage) and i only have towels and bedding in there (no wheel or bowl) I put 4 small towels and some Care fresh small animals bedding in there. My mom will not let me bring him in the house so i made sure he was warm enough. I feed him some goats milk from the pet store with a small eye dropper every (at the most) 4 hours. Is there anything else that i should do besides what i am doing? I also want to know when he will open his eyes, if he can carry diseases being this young and if I should let him go when he is older. I am working on getting my mom to let me bring him in the house very soon. I honestly don't think that he can carry diseases being this young and that i should not let him go if he is too attached to humans but if he seems to want to leave then i will let him go but i want to know what you think. He already has fur, he is not pink, his eyes are still closed and when he trys to walk he wobbles a little bit because he is so little he only squeaks once in a while and it is very quiet. P.S. I rub is bum to make sure that he pees with a Q-tip that has warm water on it and i also wipe away any milk on his face.. wet or dry. Thank you for your help :)