Is it possible to use Java to build a web browser like Internet Explorer that will open all the web pages and display all the contents?
The only valid answer to that question is:
Yes, it's possible to use Java to build a web browser.
However, a web browser is an exceptionally complex piece of software. Even Google, when building its Google Chrome browser, used existing technology to do it, rather than inventing their own browser from scratch.
If your goal is anything other than building and marketing your own browser, you may want to reconsider what exactly you want to accomplish, in order to find a more direct approach.