Yes you can do that with Ajax, with some Javascript things. The website Remember the Milk for example enables you to use it offline thanks to this, have a look.
I think you need to take a deep breath and start at the top of this forum. There's a lot of reading to do before you can even understand the questions you want to ask.
AJAX is technically just a particular style of writing javascript. Javascript has been in use with HTML on web pages to script actions practically since they evolved beyond simple text browsers.
No, you cannot magically turn a webpage into an app. You could create an app that contains a webview to locally display your web pages, or display some pulled from a server.
But what would stop your users from just visiting the mobile site with Safari instead of buying your "app"? Nothing.