Thanks a lot!
So, I've been trying those:
1/ I tried to swtich to cassiopeia by activating it as my default template. However, when I get to the downloads page, my Gantry template gains the upper hand, and I can't find out why. Tried to modify the template name in the menu parameters. In vain. So, I basically can't figure out what makes it impossible to have the template Cassiopeia with my downloads menu...
2/ I see that there are 2 versions of bootstrap indeed. When I look into the PD css, I see that:

Now if I unpublish Bootstrap.min.css (the old bootstrap version??), the modal popup appears but this is what I see:
instead of:
What can I do?
Can I do without this Bootstrap.min.css file? Where is it called for? In other words, does PD need it to work?
3/ Yes, we happened to do a bit of formatting. I sent you the code just for you to check if, by any chance, there might be a conflict between what we inserted in the custom.scss file
Well, good luck with floods! I hope you'll make it through because it really seems to be dramatic and disastrous!