Once I complete a sprint and I need to start a new one; how can I carry forward ongoing tasks to the following sprint?
You could select a number of rows and then move them to this other sheet, if that would work for you (see Move and Copy Rows).
Another alternative would be to create a Report using both separate sheets as the source, bringing in rows from each of them that are currently ongoing. This webinar goes through how to create a Report.
If neither of this would work for you, it would be helpful to see two screen captures of your current set-up, but please block out any sensitive data.