Here are the answers to the questions based on the passage:

1. **When did Churchill first become Prime Minister?**
- Churchill first became Prime Minister in May 1940.

2. **By what did he inspire the people of Britain to continue with the fight?**
- He inspired the people of Britain by courage and determination expressed in his speeches.

3. **How long was he a Member of Parliament?**
- He was a Member of Parliament for 63 years.

4. **When was his Conservative Party defeated?**
- The Conservative Party was defeated in the general election at the end of World War II.

5. **How old was he when he resigned as Prime Minister?**
- He was seventy-seven years old when he resigned as Prime Minister in 1955.