Your dad has had his affected kidney removed, can I just check that you mean 6 cms??? and not inches, because that's a rather massive tumor and doesn't relate to a stage 2. Generally speaking a T2 tumour is relatively treatable with little after effect, as in spread, because there's no lymph node involvement and no secondary cancer noted. Usually spread relates to a different staging, and I assume some radiotherapy has been done to coincide with the surgery? Depending on when the cancer was removed, your dad should be seen by a cancer specialist at agreed regular interval, for approximately 2 - 5 yrs. It is after 5 yrs or so, being tumor free, the patient is considered cured.
It's perfectly normal for you to worry, as we all do with our family, but cancer is a highly monitored disease and cancer specialist are more abundant. Monitoring patients with cancer or after cancer treatment is usually common place and done so to maintain the treatment results. Your dad is in good hands.
All the best.