How to automatically unpublish / move to archive an article or node? I need to have a functionality that allows users to create an article and choose for how long the  user wants it to be published (for example 7 days or 2 weeks). After this time the node will automatically move to archive.

How can I achieve this in Drupal 7? I know that there were some modules (Node expire?) in Drupal 6, but I am not sure about Drupal 7. Any advice?
I think you can easily archive your goal with a bunch of module.

I guess with Rules that gonna help you to make some actions when the article will be unpublished. Flag module will help you to set a flag 'Archived article' and finally Scheduler that let your user to choose when the article will be archived.