What' you describe is that your blog is working correctly. Sticky posts are stuck to the top of the main page of the blog ie. to the running page for posts. There is only one running page for posts in a blog and all other posts appear below the sticky post in reverse chronological order. The only way not to have the posts display on the front page of the blog is to create a static front page and apparently that's what you have done.
Pages are static. They sit outside of the blog structure and you cannot post to multiple pages in any blog. There is only one main page for posts in a blog and all posts will show on the main blog page. There is no way to exclude posts from the main posts (blog) page.
What’s critical is:
(1) a clear comprehension of the differences between pages and posts > http://en.support.wordpress.com/post-vs-page/
(2) a clear comprehension of the fact that there is only one dynamic page in a blog for posts and we cannot post to more than that one page. But we can create the appearance that we have posted to more than one page. We organize posts by assigning categories to them. You can either put the categories widget into the sidebar, or you can create a custom menu and add the categories into the custom menu.
If you do not want all the posts to show on the main page, then you can create a static front page for your site. If you wish, you can also create a “blog” page, but you do not have to if you do not want to.
Choice 1 static front page.
Choice 2 running page for all posts on front page.
It’s one or the other. There are no other choices.
If you choose Choice 1 static front page then you have to create two pages. One for the static front page which you can call anything you choose example “Welcome”, and one for the blog posts to appear on which you can call anything you choose example “Blog”. Adter your do that you go here . Settings > Reading and make the designation change and click “save changes”.