Question: Why did Shere Khan kill Akela?
Answer: Shere Khan was angry that Akela would not turn over Mowgli to him. It was retaliation.
Question: How did Howard and Madeline not recognise each other?
Answer: They did recognize each other (at one point he goes to her house without asking her address). After the divorce, Howard said that he wished they were strangers again. They literally behaved as if they never met each other before (even though Madeline is gently pushing to move past being strangers - for example, by guessing he's divorced).
Answer: It was a threat to Mowgli, hoping to lure him back in grief and to save the younger wolves from the same fate.