1. Not with a script. A plugin can do it, though, I believe (better ask at the Acrobat SDK forum about that).
2. Yes, it's possible, but it's not easy. You would need to create a dialog object with all of these fields, and then the user will be able to make their selections and you could use it to save the file. However, saving a file requires a trusted function, which means you need to either use a script that is installed on the local machine of each user, or certify the file.
Regarding the dialog, have a look at the execDialog method of the app object. There's a detailed description there, as well as several examples.
You cannot add a new menu item to another user's computer unless you have them install a script. But you can add a floating toolbar button.
You can add a new menu item using a script, but not a new menu, which is what the OP asked about (if I understood correctly).