@M26K, Welcome to the HP Support Community!
No, an empty ink cartridge will not cause these errors. However, it has to be replaced for you to resume printing.
Restart the wireless router, the printer, and the MAC
Make sure the printer and the MAC are connected to the same wireless network.
If the printer is not pulling the paper for copies, and if you have tried the steps mentioned in this document - An 'Out of Paper' error displays, printer does not pick paper, I'm afraid this could be a hardware issue with the printer.
Update the printer firmware
Click here to download and install the latest printer firmware from your MAC.
Click here to know different methods of updating printer firmware.
If the issue persists, please reach out to HP Support in your region regarding the service options for your printer.
If the printer is out of warranty, I suggest you upgrade the printer. You may visit Hp Store to check the available printers.
Keep me posted for any other assistance.
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Have a great day!
KUMAR0307
I am an HP Employee