Newborns have hiccups quite often. No one knows with absolute certainty why this is, but hiccups are caused by reflex stimulation of the vagus nerve to the diaphragm. We assume the frequency of hiccups in newborns is a feature of their neurologic immaturity. Hiccups are harmless, do not bother the baby in the least, and go away in a few weeks. This reinforces rocking or nursing to sleep, which leads to the predictable problems of poor napping and erratic daytime schedules, and night waking and crying at around 8 months - leading their mothers in desperation to my most excellent video.
Umbilical cords separate in two to three weeks on average.
They are wrong. Care of the umbilical cord is one of the topics about which doctors disagree. I have also never had a serious cord infection in several thousand babies. In truth, the only reason to worry about the cord is that modern babies wear diapers with plastic liners that predispose urine-soaking of the cord. That moisture allows germ growth.