The Question and Answer section for The Ramayana is a great resource to ask questions, find answers, and discuss the novel.
Anjana is Hanuman's mother.
The father of Hanuman was Kesari. That is pretty much what the texts say.
Dasaratha granted Kaikeyi's request for the services she rendered him in the war when she repaired the broken wheel in his chariot. Kaikeyi aided Dasartha in the war by acting as his charioteer.