To be refers to a state or condition and become refers to the process of reaching that state or condition.
I am fine now. I'm happy and I'm relaxed. I'm lying in bed reading a good book. It seems that the nieghbours are having a party. The noise is beginning to bother me. The noise is getting louder and louder. I'm started to feel angry. I'm getting angry. I'm becoming angry. Now the noise is very loud and I am angry.
A - I used to go dancing every weekend but now I don't.
B - When did you go dancing for the last time? - is the same as - When was the last time you went dancing?
A - The last time I went dancing - or - I went dancing for the last time in 1995.
John bought a hat yesterday.
subject question - Who bought a hat yesterday?
object question - What did John buy yesterday?
When did John buy a hat? Both the subject and the object are included in the question.