I am trying to edit a form by removing one text box and moving another text box up on the form page.

I added a text box called Website address that I need to move below business name. The move icon displays on hover but it will not move.

I also need to delete the text box underneath that, but the three links that usually appear to the right of the box to edit and delete are not there.

May I ask what device and browser are you using to edit your form? If you are using Chrome on a touchscreen device with Windows 8 or 10, it could be possible that Touchscreen support is enabled on the Chrome browser which may be why you are unable drag or move the selected fields.

Please try disabling Touchscreen support function in Google Chrome by navigating to chrome://flags/ and disabling Touch events to see if that works. Or you can follow the steps on this guide: Google Chrome - How to disable touch input 

As for the three links on the right of the box, it seems that the width of your form extend the width of the form builder, which may be why you are unable to see them.

To resolve this, please click the Design button, select Styles tab, and reduce the Form Width from 900 to 500.

Save the changes and they should now be visible as seen here:

If you need further assistance, please let us know.
Regards.