Thanks for trying to help, contentiskey
I’m a bit of a muppet but here goes:
1. Yes, I have everything backed up; I use Duplicator
2. Umm, I don’t know what ‘via FTP’ means, I’m sorry
3. Possibly
4. X-theme is active – the files are obviously all still intact over at Bluehost
5. Yes. I’ve just downloaded a free parallax theme and uploaded it into WordPress.
I guess this means the fault lies with the Themeco download!