Can my customers open the invoice on their phone etc. Or does it have to be a desktop?

Hello there, @simon-ampelectri.

Your customers can view and open an invoice on both mobile phone and desktop browser though it requires your customer to click many links to open the full invoice if he’s using QuickBooks Self-Employed (QBSE) on the phone.

If you’re using QBSE on the browser, all you have to do is to click View invoice and the full invoice will automatically pops-up.

If your customers can’t view or open the invoice, I recommend clearing your cache browser. Most common display issues are caused by too many cache files in the browser. 

You can also use this handy article to learn how to customize an invoice in QuickBooks Self-Employed: Customize invoice.

If you have more questions, you can always tag me or post a new question in the Community.