No additional QuickSight fee for scheduling full SPICE refreshes.
Yes, your costs are primarily (a) SPICE storage at $0.38/GB-month and (b) data source query charges (e.g., $5/TB for Athena, S3 GET request fees, Redshift RPUs, etc.).
Frequency of refreshes does not directly increase QuickSight costs, but more frequent queries to your data source can drive up external query fees.