Is my church a non-profit organization?

Your church is almost undoubtedly a nonprofit. You can check with church secretary or pastor to be certain. However whether that makes it a place that you can do your hours depends on whether whatever requires the hours accepts a religious congregation as a community service place. Some will some won't. If you can help with a food ministry if the church does that, outreach to kids or seniors in the community or something that serves people who are not part of the church that is more likely to be accepted.