You've inspired me to dust down my Colloquial Icelandic book and seek out the login for the online course I started.
Yes! That's the exact book I started with. Go for it!
For how many weeks is it dark day and night? Are the winters not hard to bear in terms of cold and dark?
It's never pitch dark day and night, even around the winter solstice we have a few hours of gloomy half light. From November to January it is pretty dire, though. Yes, it is very hard. It is the worst thing about living here in my experience. I feel quite sleepy and down for a lot of the time over those 3 months. Luckily the light summers are amazing and make up for it. Even when it is not sunny, I love all the light.
It's not actually that cold here in the winter, though! Rarely gets below -4 or -5, which is really quite easy to handle. It's not like Sweden or Canada or those places which get really extreme low temperatures. The winter storms can be very tiresome, though.
*What are kids surnames when their dads not around?
A matronymic is used instead of a patronymic. Last names are traditionally formed by taking the father's name in the genitive case and adding on 'son' or 'dóttir', so you just do the same process with the mother's name. E.g. a woman named María could have a son named Helgi Maríuson.
Some Icelanders have actual surnames, e.g. Bergmann or Blöndal. So I suppose a single mother with a surname would probably use that for her children. But it's relatively rare to have a surname.