The best way to keep track of posts you've made is to flag the thread you posted in. If you click the symbol next to the title it should turn green, and then you'll be able to find the thread in My Flagged Threads whenever you want as well as be notified when somebody else responds.
Unfortunately the site currently does not have a search feature, so a cursory glance at the board will probably have to suffice.
"Also is there a search feature on this website so I can avoid making repeat topics?"
To expand on what has already been said, the best way to avoid making repeat topics would probably be to look at the sticky threads on the board your are one. These are found at the top of page one on every board (if there are any on that particular board), and are shown by the icon. There may be a sticky thread that may be suitable for what you want to post. For example, if you wanted to post on the New Leaf Trading Board asking for fruit, there is already fruit thread sticky on that board that you can use instead of starting a new topic. However, as Chris mentioned, there is no search feature currently for this.