Google has stated that they intend to keep every file they've hosted available indefinitely, so you shouldn't need to worry about them disappearing.
Firstly, if you are using a caching plugin, flush the cache or temporarily disable it to be sure it's not doing anything. That said, I've done my best to make Use Google Libraries gracefully step out of the way when things are not as expected. While not, perhaps, giving you the greatest benefit it helps ensure you site doesn't just flat out stop working.
In general, anything that calls wp_register_script and/or wp_eneque_script before 'init' causes trouble for Use Google Libraries. I've made an effort to force it to try and run anyhow, so please report any issues with this. If you have 'WP_DEBUG' enabled, a message will be logged letting you know this is happening.
Please see the section on Incompatible Plugins and Incompatible Themes for specific information.
The same way you use them when Use Google Libraries isn't installed using 'wp_enqueue_script'. In fact you should develop your theme or plugin without Use Google Libraries being enabled at all, then test it both ways.
Assuming some other plugin or theme isn't the cause, Use Google Libries does it's very best to ensure your site behaves as it should when using the stock WordPress scripts. If WordPress is asking for a version of a script that Google isn't hosting, then it will continue to use the WordPress supplied version.
No. Use Google Libraries doesn't do that because it would almost certainly break WordPress. Even if it didn't, the less 'version specific' URLs supported by Google's CDN set a short term 'Expires' header, so there wouldn't be much point.