Question

1. While he extended his hand, he smiled brightly.
2. While he was extending his hand, he was smiling brightly.
(Are both okay?)

3. When he extended his hand, he smiled brightly.
4. When he was extending his hand, he was smiling brightly.
(Can we use 'when' instead of 'while'? What is the difference between them?)

Answer 1

All four sentences are fine. Look up he words "when" and "while". In the contexts you have used them, they mean the same, but look them up.

https://www.merriam-webster.com/dictionary/dictionary