How effective are standard treatments in eliminating the cancer and preventing recurrence?

It depends... It depends on the type of cancer you are talking about. With respect to pediatric cancer as a whole, we cure ~80%. Some cancers approach 100% cure, while others are ~10%. We are constantly performing research and clinical trials to help those we currently cannot cure.
Steadily improving. In terms of winning the battle against cancer, we passed the 50% mark about 5 years ago. We are now winning the battle about 65% of the time.