Learning Drupal Module development depends on how you like to learn things, you have some great books like Drupal Module Development, video tutorial services like buildamodule.com or drupal.org information like Drupal API reference or the examples module as pointed out by underq.
I find it is best to try and use a combination of different mediums, books for example give me good theory / in depth overview on the many aspects of Drupal development while the videos give me more of a hands on / visual understanding. Then follow this up by actually building modules using this stack and the API reference / docs for help along the way.
To answer your questions directly
- I would start with Drupal 7 as this now has taken over Drupal 6 in market share
- The API has changed somewhat but this is reflected in the API reference material
- As above