Hi, you are talking about the Code Hints popup box.
I don't think there is a hotkey to make it popup at anytime, but I'm not sure. I know for a fact that it is supposed to give you a list of tags which will work with whatever element you are working with in design view ONLY.
As long as you've got your mouse inside the element you want to work with, it should popup, if it doesn't just hit your space bar - so it'll know you want to add a new attribute.
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The "hints" that it shows you are most likely taken from Dreamweavers tag library... (Preferences > Code Hints > Tag Library Editor) Persoanally I would not screw with this, but if you are using some custom tags which you use often, which the code hints popup isn't showing - you can always add them to DWMX yourself 🙂
Also too, DWMX doesn't recognise the ".php3" extension by default, but you can make Dreamweaver read this as a PHP file as well, if you know how to get to the XML files.
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It'd be nice if we had this little code hints box in WYSIWIG view too, but oh well. Maybe next version.