Can only really guess about the answers to these questions. I would have thought Panda would be fairly good, but it is certainly possible Avast is detecting what Panda didn't. If you Google the name of the malware indicated, it is real, and a worm that exploits vulnerabilities. Avast appears to have stopped it in its tracks. Nice.
I'd suggest you see about getting all your software up to date. Out of date stuff on board is one of the likely routes for any web based exploit. Have a look at
http://secunia.com/ and try the online scan out. (You'll need to "OK" the loading of a Java applet.) The scan may reveal much about the condition of your software.
Not a bad philosophy, that of not clicking on popups. When Avast gives you an alert, it is accompanied by a sound, and identifiably Avast. Like the info box says, no need to panic, though. Closing it quickly would have made no difference to the payload installed, had it been a bogus.
It's safe to look at the Avast alerts, and take the appropriate action, in this (and most cases) send it to the chest.
You can leave it in the chest indefinitely. It isn't going to escape; can do no harm there.