1) No, only less than 50% of all girls bleed when having sexual intercourse for the first time.
2) Most girls suffer from mild pain when the hymen gets torn during their first sex.
3) If a girl bleeds, the blood originates from the torn hymen which is located about 0,5 inch inside the vaginal opening. Thus, the blood does NOT come from the vagina, but from the hymen, which belongs to the vulva (outside genitalia).
4) "Why?": The vaginal opening is covered by a thin membrane, which hole is wide enough to let fingers or tampons pass, but which is so narrow as to be torn when larger objects like a penis enters the vagina. This membrane is called hymen.
I have added a nice link to the "cool nurse" which explains everything in laymen's terms.
