1. You are posting in the wrong forum. Please post questions about using jQuery Mobile in your project on the 'jQuery Mobile" forum.
2. As I understand it, this isn't *needed* at all. If you are doing cross-domain Ajax requests, then, yes, you need this, along with some PhoneGap setting as well. (Check PhoneGap documentation or ask on a PhoneGap forum.)
3. If you use a mobileinit callback, then, generally, (not specific to PhoneGap) the script should be included on every page. It is better to put it in a file rather than put it directly in <head>.
4. In a *properly written* PhoneGap app using jQuery Mobile, you would only need this on the index page. However, I've seen very few properly written PhoneGap apps that use jQuery Mobile.
If you use data-ajax="false" or data-rel="external" anywhere, then you should include it on every page.
In PhoneGap, the user cannot "refresh" the page or save a bookmark, and so they will always start with the home page, and the document will never be reloaded. In fact, you can actually leave out all of the scripts and CSS on all but the index page. But if you use data-ajax="false" or data-rel="external" that is all out the window.