Thank you for your interesting questions. I think firstly it may depend on what sources you are using, secondly on your definition of "advanced" and thirdly what time span you are talking about.
a) Possibly South Africa. This country does however have a legacy of apartheid in which not everyone lives a standard of living seen as "advanced". Israel has a lower fertility rate then SA but that is also a country with apartheid and the inclusion of Palestinians as second class citizens (those living within Israel itself) complicates matters.
b) I couldn't detect a country that had this type of increase. Yes, Russia following the collapse of Stalinism did see a decline followed by a rise, but this is on the decline again. One large country that seems to have been consistent for some time is Iran - but compared to say 1988 it has also collapsed.