hi AK,
i'm a jun 10 mother. baby currently about 7 weeks old. kapo here a bit, dun mind me. i think your baby is being fed too much. my son was drinking about 40ml to 60ml during first few weeks. if they don't have enough, they will keep crying, that the signal that they need more FM. my son is partially FM and partially BM during his 1st month. Now, majority FM. If they have too much, according to my PD, they will puke out, then by the next feed, we should reduce the amt of FM. cannot give the same, must reduce.
As for the red backside, it could be due to disposable diapers. newborn skin very sensitive, if you find that the backside is turning red, better change to cloth nappy. my son is using cloth nappy during the day and disposable during the night.
i find your nanny is too irresponsible, she is just looking at making her job easier, rather than really caring for your newborn. if u can manage, maybe u should just ask her to go. no point, leaving your newborn in her hands. if cannot, then tolerate it for a while.
Try to let your newborn suckle, my son finds that milk bottle is so much easier, refuse to latch and after struggle with him for a few feed, i gave up and gave him FM and express BM. My milk supply drops and after 1.5 mths, i don't have much BM left. it's a disappointment, but nevermind, just concentrate on being a good mom.