Question 1: Java and JavaScript are two different languages. JavaScript is a dynamically typed language where Java is strictly typed language (i.e. you have to define variables as int, string, etc...). Every browser except for screen readers should have JavaScript turned on by default. The thing to remember is that users have the ability to turn off JavaScript if they so choose. The reason they turn it off is because during the 90s JavaScript was used in the wrong ways such as creating pop-up after pop-up windows and other mischievous things.
Question 2: You should always develop your website to work without JavaScript turned on. JavaScript is like icing on the cake. It is the fancy behavior that your website has. The technique of developing your website to work with JavaScript turned off but be more "enhanced" when it is turned on is called "Unobtrusive JavaScript". Basically, it means that your users can get to your web pages content without the need of JavaScript. Search in Google for "Unobtrusive JavaScript" and you will find a plethora of information and techniques.
Here are just a couple links to get you started:
A List Apart Behavioral Separation
Easy as Pie - Unobtrusive JavaScript
Question 3: Yes. If JavaScript is turned off then your Ajax methods and jQuery library will not work.
Do some research regarding this topic. You will find a lot of information that will help you in your journey of discovering Unobtrusive JavaScript.