Hello,
Re Q1: I'm not sure why the printer is reinstalled. Some Office updates may cause such issue.
Re Q2: Please try to use "Remove driver and driver package" when you try to uninstall the printer. To do this, Please follow:
1. Go to Control Panel > All Control Panel Items > Devices and Printers.
2. Click on File and then select Server Properties.
3. Click Drivers tab in the Print Server Properties
dialog.
4. Highlight the "Send to Microsoft OneNote 15 Driver" and click Remove button.
5. Select "Remove driver and driver package" and click OK.
Please also try to delete the "Send to OneNote 2013" subkey in Registry Editor to check if it helps:
HKEY_LOCAL_MACHINE\SYSTEM\CurrentControlSet\Control\Print\Printers\Send To OneNote 2013
Please let me know the result.
Regards,
Steve Fan
TechNet Community Support