Thanks.
I have started the restoration, since this problem appeared very recently. And I will also try to go through your advices to get it all fixed.
Thenks Keith !
I will get in touch with Blue Host again (they told me they felt like it was a theme issue, but I will contact them again).
Regarding your advice of renaming the theme folder, in order to deactivate it, I can do it for sure. But what is the next stepd after that ?