Dp you celebrate any other special occasions?
No. What for? They probably don't know themselves when they were born.
The ones that are believers may celebrate their deity's day or their favourite daedra or just the local holidays: http://www.uesp.net/wiki/Lore:Calendar#Holidays
Absolutely. They're all a given.
Before Skyrim, I gave them a birthday based on what starsign they were born under. Now it's just sort of at random. Family doesn't really factor much outside of playable siblings/relatives.
In the games that included Birthsigns I've assigned birthdays to my character. I've used my actual birthday or a day based on Daggerfall's summoning day either of my favorite daedra or if there was one the summoning day of the daedra associated with the birthsign I wanted. Then there are times in which I just used the real month and day that a character was created. When I did that I would either accept the associated birthsign or take the Serpent instead.
With the games that Birthsigns played no significance I didn't bother with it and just assumed I was born.
I don't. I barely remember my own birthday, so my characters pretty much have to fend for themselves.
The people in Tamriel are very much able to do that;)
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Yes I do,sometimes random, since I also choose the correct Brithsign.