Is it true that Cherrytail was Firestar's apprentice?

Yes but only temporarily. She later then became Sharpclaw's apprentice in Firestar's Quest. Its not the Cherrykit in Thunderclan who people might think will become Cherrytail and Firestar's apprentice but the kittypet who joins Skyclan who is know as Cherrytail in Skyclan's Destiny. Her brother is Sparrowpelt who was know as Boris as a kittypet.