JFBLogin module problem

The JFBCLogin module does not use it's own stylesheet. It inherits styles from your template or from any included stylesheets on the page. The only reason the module would look different depending on the page is that there are different styles depending on the page your on, likely from an included stylesheet for the specific component being displayed.

While this doesn't fix your issue directly, hopefully, it helps you narrow down the cause. If you can't find it, feel free to link to 2 pages, and we can quickly tell you where the different styles are coming from.

The reason the checkbox is moved to the lower line (on the Community Page at least) is because of this line:
label {
display:block;
}
In www.tuttotesti.com/components/com_commun...efault/css/style.css

display:block makes the contents of that line by by itself, and moves any other content to the next line. (Not the real CSS definition, but close)

I'd recommend adding the following to your template stylesheet, which should fix the issue:
#tpblock-left label {
display:inline;
}

It doesn't seem like anything else on the sidebar is using labels, but if so, this could cause other issues.

Hope this helps!