Here are the correct forms of the verbs and words:

1. When I was a kid, my father (make) **made** the big decisions in my family.
2. I listen to music in English (improve) **to improve** my skills.
3. It's essential that Peter (note down) **notes down** all the important details from the meeting.
4. My friend lives with her **extended** family. She lives with her parents, grandparents. (EXTEND)
5. You can turn on the English subtitles to understand the actors **clearly**. (CLEAR)
6. English is often a common **language** used for communication between people from different backgrounds. (LANGUAGE)