1) Which 'demo sites' are you talking about? Do you mean this site, in the top right with "My Account" or somewhere else? Just checking what you mean. This site has a little bit of extra CSS to do our menu. We're hoping to get it in a future release, but honestly causes other conflicts with templates that we know a lot about, so we didn't want to include it yet due to the known support problems it would bring.
I typed all that, and then looked at your site and see the hover drop down is working now. I'm assuming you got something going that works for you, but if not, let us know.
2) As above, your menu is vertical now, so I think you're good. Our CSS can't really rely on a template to set the colors, because if the template doesn't have the right styles, then no colors (or conflicting colors) will be set. It's a tough game we have to play of either over-specifying the CSS (to make sure everything works exactly how it should) or under-specfiying it to allow the template to set some styles.. but, if it doesn't, then, again, we get in trouble. In the future, I'm sure we'll have to have either some default template's for the CSS (dark, light, red). Alternatively, we may have to add 20 extra settings in the module to set button color, menu color, background color, etc. It would get complex fast though, so that's not something we really like either.
3) There is no direct URL you can use in Joomla to log the user out. It has to be generated on each page load for the specific user logged in. That's why we have the special sclogout trick in our code which will replace that with the correct logout link for the user in that session. The PHP for the link would be:
$url = JRoute::_('index.php?option=com_users&task=user.logout&return=' . base64_encode('index.php') . JSession::getFormToken() . '=1');
Hope that all helps,
Alex
Show User Menu - how to make a same one as the demo
