I can quite safely say that you are not the only one. I myself have had this happen repeatedly for about the last 15 years. I even started keeping a dream diary to prove these events to others. Keeping the diary actually increased the number of occasions.
Usually in my case the dreams are perfectly mundane, but there will be something unusual about the situation, meeting a new person for the first time, starting a new job (and not recognizing the building after the dream). Often like yourself exact details may be a little out. Names might be slightly out, almost misheard, however visually the dream is perfect. Also the dream is identifiably different to a normal dream, I can wake and think 'Yup that was one'.
When I was younger this sort of experience terrified me. When the 'deja-vu' occured I often began to panic because of the eeriness of it all. But after the sixth of seventh time it happpened I began to relax into it.
Eventually I started using the knowledge to my own advantage a little.
I dreamt about every girlfriend before I met them, which is an interesting way to start dating, knowing that you are not going to be rejected. I did tell each of them about it- I felt it would be kind of dishonest not to. One, however, panicked a little and dropped the relationship, which kind of threw me but four years later we dated for a while.
I've never tried winning the lottery or anything (I don't gamble generally) when I have played I've always see myself losing in advance (not at all helpful), and don't remember the numbers anyway (I'm dyslexic, especially with regard to figures).
Nor am I at all interested in proving to anybody that I can do this, infact if I try it kind of goes away for about six months to a year! I'd rather have the heads up than definitive proof. That said I've spooked plenty of people, and made a few believers along the way.
There was a time when I was younger and more scientifically minded (back in my physicist days) when I sought a more rational explanation. The normal one that I would come up with is that the brain is a remarkably astute calculator that can process an awful lot of data. It is possible that in the first situation you were acting on subconciously noticed and processed cues. And constructed the day ahead. You may have processed the name from an overheard phone conversation , or subconcious lip reading, hence the correct feel but wrong starting noise.
The Bird case is less easy to explain away, in this instance it is easier to use occams razor to say either you are confused about the sequence of events (you told your friend before or after finding the bird about the events you'd forseen?- I assume before from her reaction) or that you precognitioned the future. Just because there is no clear scientific principle at work here does not make it impossible. It just means science doesn't know everything yet... Since two physicist have a hard time deciding if time travel is possible or not, I can say precognition is more possible than physical transportation.
As to why these precognitions are so mundane. Your future (in general) is more full of mundane, and slightly odd events than life threatening adventures (I hope)
It's therefore not too surprising that if you look forward a random space of time your more likely to see a reasonably normal event rather than a future car crash say.
Personally I think this happens a lot more than people admit, generally most people ignore or don't remember their dreams. I think if more people kept dream diaries we'd know a lot more about this phenomena.