If you purchase red harvester ants from us your colonies expected to live from 2 to 6 months sometimes longer sometime shorter but thats about the general time frame.
The Queens her main job is to have babies. She's not required for your current workers to survive. When a queen is present however their main job is feeding her and keeping her happy.
One thing we do suggest when setting up your ant farm to to daily give it just a little crack of air from the top and it will make your ants much happier and livelier.