No, you cannot post to a page. You can use your "bulletproof" page to link to the post, or even multiple posts.
First, though, I really recommend that you work through this tutorial to get acquainted with this WordPress.com platform:
Now, to your question.
Here is an excellent article about why you cannot post to a page:
(be sure to read the preliminary links Panos provides:
post vs page )
The article links to how to make a custom menu. Read that, and there is also a wp.com support article about custom menus:
I hope all these links don't overwhelm you—we were all beginners once, and because wp.com has so many options and possibilities it may seem daunting. Just go one step at a time…