Oh god, sometimes I hear concert A's as I'm waking up in the morning.... still. At one point I dated the concert master (oboist, never date an oboist) and that's what really drilled it in.... I was not just paying attention to the note, but to her too.
Nope, but from teaching a sightsinging class for two years I found that pianists and violinists tend to have better aural skills when they arrive in college than other musicians (in general, not a scientific survey, just observation and obviously there will be exceptions).
I suspect it is because these folks probably started playing a lot earlier than others.