That would be התפרקה (broke up) or התפצלה (split up). With נפרדה I’d expect it to split up from something else, like, הקבוצה התפצלה\נפרדה מהקבוצה הגדולה יותר.
Second this. פרד is used as 'break up' (sexual relationship) or in a more mundane 'to part' as in, we went to a movie and then parted ways. When speaking about a group ceasing to be, פרק would be the way to go
You basically made it passive. Thanks for reinforcing this. The group was broken up a year ago (by some outside cause or influence, at least).
Is there a difference between "one year ago" and "a year ago"?
There's no big difference (If there is any at all!), "One year ago" is usually more "specific" - But you can use both without any problems!
I use "one year ago" and it is not accepted!