Yes it is safe in the fridge, it can stay in there for up to 24 hours. I will say this, they say if baby has drank out of bottle to throw away one hour after feeding time began, because of bacteria. And if feeding doesn’t begin in two hours after made to store in fridge for up to 24 hours. I honestly never followed that, if baby didn’t finish bottle within 2 hours I put it in the fridge until hungry again. 8 months old, and nothing ever happened (not saying it can’t)
As long as it's thrown out after an Hour I do believe so if he wakes up with in a Hour then yes But if it's later then No it can cause thrush. Idk about unranked bottles