In Manage, then Records, press "Download CSV" to download whatever view you're looking at as a spreadsheet. The training matrix can also be downloaded as a PDF.
For certificates, tick the ones you want in Completions. "Download as one PDF" puts them all in one file to print. "Download as separate files" gives you a ZIP with one PDF for each certificate, named with the person, the course and the date. You can download up to 200 at a time. For one person's certificates, open their page in People and press "Download all".
If an inspector, a trust or a local authority needs to see your records, "Share with a school" in Records makes a read-only link that stops working on a date you choose.