Did you try to use the cursor keys to select an item in the drop-down list instead of using the mouse?

There is also a "Fill Login" item in the right-click context menu (you can open the context menu with the keyboard).

I'm sorry, it seems like you don't undestand me. I have attached some shots for better understanding. It's basic hide/show login block on hover behavior. (if cursor is out of block range - block wil hide)

Also you can look at this yourself, please welcome. http://www.my-art.com/ On Chrome it works like a charm.

No problem here with the website and the page inspector still shows this element even when the pop-up closes when I go to the inspector.

Autocomplete for an input field in that pop-up should work without problems.

If there are problems then check for issues caused by an extension.

Start Firefox in Safe Mode to check if one of the extensions ("3-bar" menu button or Tools -> Add-ons -> Extensions) or if hardware acceleration is causing the problem.

• Switch to the DEFAULT theme: "3-bar" menu button or Tools -> Add-ons -> Appearance
• Do NOT click the "Refresh Firefox" button on the Safe Mode start window

• https://support.mozilla.org/kb/Safe+Mode
• https://support.mozilla.org/kb/Troubleshooting+extensions+and+themes

You are right, but expected that green login form remains visible, that element of browser suggestion must belongs in this login form block like a html or pseudo-html. I dont know what is it. It's wrong behavior if your inner element doesn't belong in this block.