I suspect that for what you are trying to do, you should be an affiliate of your parent organization. Check with the parent organization for their group exemption letter. See https://www.irs.gov/pub/irs-pdf/p4573.pdf
Assuming you get your own the EIN and are operating under the parent's charter, you will have some filing requirements based on your level of financial transactions. You may need to file a Form 990, or a Form 990-EZ. Most small organizations would use the more simple Form 990-N (e-postcard) if their gross receipts are $50,000 or less. Your parent organization should normally be assisting you with this.
