Well – decided to go for a standard theme, so the formatting bugs seem resolved, as do the social media links, but still cannot find 13 years worth of uploaded images and media anywhere on the server.
Only solution looks like progressively re-finding and re-uploading each important image – quite a time-consuming chore – ho hum. [Update - on a first 80/20 pass I've re-attached the top 20% with 80% of the value. That will have to do for now - if you find any interesting images missing, let me know.]
Other minor item is to organise the page links in the header, since the standard theme simply defaults the top level pages, whereas I had manually linked pages beyond the WordPress-managed blog pages previously.