1) when you are in edit mode for one symbol, go into edit for the next symbol in library
2) automatically put cursor in the instance name box for selected movieClip
As far as I know there are is no way to put shorcuts for moving around "inside of the library panel"
A duplicate and edit shortcut would sure be nice though. I can't even find where you would do it in custom shortcuts.
The examples you have listed do not have shortcut keys because they are not default tasks inside of the IDE. That being said you can create ways to do those examples using JSFL to first create a command and then assign a keyboard shortcut to that command. As an example I will include a script for the second item in your list.
There currently isn't a way to tell the IDE to send the cursor to the instance name box in the properties panel, but you can get around that by using JSFL. Let's make our own instance name box pop up.
Here is the code required to do this:
Save this command as a JSFL script in the commands folder in your Flash config directory and then assign a keyboard shortcut to it.