I suspect many of the people congregating in the square are not Catholic or haven't been inside a church of any denomination in years! Hence the celebrations. However, while you might think it would be nice to be a little more subdued out of respect to the recent death of the previous Pope, it's also a huge occasion and celebration of a new Pontiff - bit like VE Day was both sad and joyful.
As for your Grandma, it was very common in her generation to observe mourning more strictly - my Mum for instance didn't send Christmas cards in the year that my Dad died and that was a very commonly-observed custom, but I don't think anyone really pays any attention to those traditions nowadays.