I was wondering if it is possible to set expiration date of an article after a month or a year after it is submitted. And if so then set the amount of time to differ per user group.

Hi. You need to make a K2 plugin for this. The plugin will need to be triggered every time a K2 item is saved ( onK2AfterSave event). Then the plugin will check if it's a new item and set the Finish publishing date accordingly.