Well, I tried to install another gallery (Gallery 2... simply) and at a point in the installation I wasn't able to go ahead. The message was that, suddenly, I wasn't allowed to access to the "index.php" of the installation were I was already working on...
I'm not sure that I've understood exactly what you said above. In your opinion my host should modify something on the server ? This open_basedir thing isn't really clear to me actually, but I'll try and have a look...
And if I find time, I'll try and install something else and report here if I meet problems ;-)
And as the week-end is coming, I don't hope they'll answer me before monday... so since then, wait'n'see...
Thanks !