Alright, my bad.
I had solved my own problems with some CSS tricks, but I put some time to investigate what I reported.
CSS differentiation is actually related to a
JA-T3 template issue that I knew before.
As for any module, you'll have to add an extra space before the module class suffix itself in Module Parameters. Otherwise the module class suffix will be direclty concatenated to the "moduletable" class.
Example : with a "fpss_test" module class suffix you'll get a module (id 35) starting div like this
<div id="Mod35" class="ja-moduletable moduletablefpss_test clearfix">
with a " fpss_test" module class suffix it will become
<div id="Mod35" class="ja-moduletable moduletable fpss_test clearfix">
This will work a lot better.
Concerning the "missing module class suffix" part, I see the module class suffix does not appear when a module is placed using custom positions. It is directly added to the page starting with the fpss_container class.
My central FPSS instance (
www.chromatique.net) is placed that way. I don't know if it's joomla or template related, but that's not FPSS's fault.
Sorry for the inconvenience.