Crockett died on the last day; Mrs. Dickenson and Santa Anna's cook, who had met Crockett in Washington when the latter was a congressman, both saw his body near the main gate. Some Mexicans did claim that Crockett was captured and executed later; the 2004 movie followed that line. While it did get the details of Travis's death right, and the fact that Bowie was an invalid, the latter suffered from typhus or pneumonia, and was in bed in one of the buildings. All in all, not a very historicalliy accurate portrayal.
Oh. The widdow of Capt. Dickenson did survive, along with her two children.
The final attack, btw, took place at night. The battle ended shortly after dawn; the times given are bunk.
As to the question of changing history, most physicists think that there are an infinite number of alternate pasts and futures in which every possible event actually happened. History would remain the same in the timeline the scientists came from, but it would have been perfectly possible to set off a new one.