This was because Carlisle believed that it was something Edward had to do, morally, because Bella was 'his'. This was, in the end, quite a wise decision, because it helped Edward take steps to overcome his desires for Bella's blood.
Bella goes to Edward's house in Chapter 15 of Twilight, titled "The Cullens".
after Bella says she was lucky Edward was there charlie says "Edward? Is that your boy?"
probably
he asked him if the edward Bella was talking about was his boy
Edward uses his teeth to help with the caesarian section
In the movie "Twilight," the character Edward Cullen says "Nice kitty" to Bella Swan when they first meet in the school biology class.
Carlisle doesn't really do anything for Bella personally. Carlisle tells Edward what he thinks Edward should do.
The order is Carlisle, Esme, Edward, Rosalie, Emmett, Alice & Jasper then Bella.
In the Twilight book, Bella hears how/why Edward, Carlisle, Esme, Emmett and Alice were changed. Bella discovers from James (in the dance studio) more information about Alice's past.
BELLA EDWARD JACOB CHARLIE CARLISLE ESME ALICE JASPER ROSALIE EMMETT BILLY
Edward, Bella , Jacob , Rosalie , Alice , Jasper , Emmett, Esme and Carlisle.
If you're asking about after Bella becomes a vampire, the it's Carlisle, Esme, Emmett, Rosalie, Jasper, Alice, Edward, Bella, and Renesmee (Nessie)