Ask users what menu they want while drupal is being installed
Yes it's possible, using hook_install_tasks().

You can use this hook to create a form that is displayed to your users during the installation process; it can be a standard Drupal form and you can add as many items of content/menu links as you want in the submission function.

Bear in mind the hook and forms your implement will need to go in the .profile file, not the .install file, or they won't work.