Their warrior names are Lionblaze, Jayfeather, and Hollyleaf respectively. Lionblaze and Hollyleaf receive their names in Eclipse (Book 4 of the third series, Power of Three) and Jayfeather receives his name from Leafpool in Long Shadows, book 5 of 'Power of Three.'
Yes, she is their mother
James Warrior's birth name is Will Warrior.
Sparrowpelt was Halftail’s warrior name before his tail was bitten by a badger(I think)
Bluestar's Warrior name was Bluefur.
Dovepaw's warrior name is Dovewing. Ivypaw's warrior name is Ivypool.
Rusty, or Firepaw's, warrior name is Fireheart.
Honeypaw's warrior name is Honeyfern.
Bumblekit's warrior name is Bumblestripe.
Firekit's warrior name was Fireheart.
The elvish name for warrior is "heru".
Featherpaw's warrior name is Feathertail and Stormpaw's warrior name is Stormfur
Leopardstar's warrior name was Leopardfur.