New Year is a huge deal! There are loads and loads of fireworks. I am never in ReykjavÃk due to always visiting DP's family in another town and they are pretty crazy there - I have heard that downtown it is really something else. The enormous bonfires I think are on the 13th day after Christmas (at least they have bonfires then, maybe also on NYE in Rvk), to celebrate the end of the festive season. We go to one in Vesturbær, it is pretty fun.
Yes, a lot of Icelanders are pretty fed up of tourists. Not on an individual level and I'm sure everyone will be friendly and kind to you when you come, but there are a lot of concerns about how the industry is managed (or not managed). The annual tourist population is much, much bigger than the resident population so that causes some issues, such as exacerbating the housing crisis in the capital area and environmental damage at the popular sites. Honestly I think things need to be reigned in somehow. Some people are getting very rich off it, of course, but these people are a minority.
A lot of young people do leave (often going to study abroad and never coming home) and this is a problem for the country, but they leave for economic reasons mainly, not because it's so unbearably dull. ReykjavÃk isn't actually that boring for young people in my opinion, although of course it's not on the level of somewhere like London. I think it seems like a lovely place to be a child, because they are given so much more freedom and independence than seems to be the norm in the UK. And it's so safe. I know my DP has never had any notions of emigrating and he didn't even grow up in Rvk! Although to be fair I think moonshine did feature rather heavily in his adolescence.
I have heard of ÞórdÃs Elva, but not until after she did the talk. I don't think she was particularly well known beforehand, no.