I hope she's OK - this sounds a potentially difficult pregnancy. Although morning sickness is widespread, the acute form,
hyperemesis gravidarum, can lead to toxic reactions that need treatment. The Prince apparently left the hospital without speaking to the press.
This royal birth will be historic. For centuries, male babies took precedence, and queens usually only succeeded if they had no brothers - though the "Glorious Revolution" of 1688 brought about one exception, when the "Old Pretender" was passed over in favour of his sisters, due to the religious conflicts of the day. Now though, the older tradition is being permanently changed in line with modern thought, and the new baby will be in line to succeed regardless of sex. (This needed the consent of all the countries that recognize the Queen as their Head of State, including Canada, Australia, NZ and several in the Caribbean and Pacific)