Many thanks to John for his very speedy responses and assistance.

A couple of things I learned which might help others just starting up:

1. When responsivizer copies the modules (see the inbuilt module manager), it leaves the page assignments selected. So you need to go into those modules in Joomla itself and change the assignments- probably to say "all pages". You will probably be changing the names in any case, so that is a perfect time to do it. Most of my modules had assignments to appear only on certain pages, and naturally, these pages were on the main website and not responsivizer. The results were very variable and very strange indeed until fixed.

2. When using a custom web page, I pointed it to a menu item on the Top menu of my Joomla template. This menu was set in the menu options of the menu manager to only appear on certain (Joomla) pages (which of course did not include responsivizer pages). So, what happened instead, was that all my Featured articles appeared on the responsivizer mobile site.

I am sure the above are all perfectly obvious to others but the info might help new customers.

Best Regards,
Dave