I think it's something like, "Driving me nuts." which means "Making me angry."

It seems that "doing someone's nut in" is a British phrase for "making someone angry," and that is why I had never heard of it. So, yes, Dad is making me angry.

I don't know what "Dad is doing my nut in already" means. 2. Gunpowder is an old-fashioned ingredient used in firearms, but I think here it just means that the prescription was not understood. 3. Ministration is giving care, as in ministering to the sick, so she is not the caring type. 4. Dissolute lacking in morals, so a dissolute baby is an oxymoron, or two words that are opposites in contrast. Perhaps he looked innocent and lewd at the same time. Hope this helps.