I'll share on how it works in QuickBooks Online, Sonja7.
You can only select the month when you set up the fiscal year. You're unable to select an actual date.
Concerning the reports, you can choose the last fiscal year as the report date. It will base on the month that was set up for the fiscal year. That being said, you'll want to change the dates manually so you can get the actual day of the month.
I'll share the reference on how to memorize a report so you won't go over to the same customization process: Memorize reports in QuickBooks Online.
We're just around if you have additional questions. Please feel free to reach out to us again. Take care!