I’m having trouble downloading batch invoices. When downloading, it just downloads a “no invoices for selected period” file, even though there should be many!

Most probably all existing invoices for the selected period are just proforma invoices. Proforma invoices are not real (final) invoices – they are generated on the fly when requested and reflects current order contents (you can make changes and they will reflect on the proforma instantly). Regular invoices, on the other hand, are official documents, they are stored as PDF files once issued and you can batch download them to pass to your bookkeeper/accountant.