The song is Rose is singing is called 'Come Josephine,' but the orchestrated song playing in the background is called 'A Promise Kept.' 'A Promise Kept' is on the original Titanic soundtrack and 'Come Josephine' is on the soundtrack "Back to Titanic."

James Horner is a music composer. Most notably for the titanic movie soundtrack.

There are many online retailers as well as brick and mortar stores that offer the Titanic soundtrack for sale. Walmart is one of those retailers, as well as eBay and Amazon. One can also listen to the different tracks on YouTube for free.

You may be referring to My Heart Will Go On by Celine Dion. To find a whole list look up titanic soundtrack.

My Heart Will Go On was released by Celine Dion in 1997. It was used as the theme song in the popular movie Titanic. The song was released on both the soundtrack to Titanic, and Celine's album titled Let's Talk About Love.