Your posts: Click on your name in one of your posts and you will get a drop down menu. One of the items is "Find more posts by" and that will take you to a list of your posts. If you are looking for "Replies to your posts", I don't believe that is an option.
Search Box: The search box is at the very very top of the page, in the right corner. There is also a drop down search in the top (main) blue menu bar. (Sometimes I forget how far up it is and usually end up using the one in the menu bar.)