More specifically, I would like to know which topics I have already posted and which I didn't.
That's what that "little face" being present in the left-most icon means (that you've posted in that topic before):
(In an upcoming patch, I'm considering making those face-containing icons clickable: The idea would be that when you click on it, it would open the topic, but with just your posts visible, so that you can easily see the things you've already said in that topic. Seems like an odd feature on its own, but, it's part of a bigger patch to allow quickly seeing only the posts within a topic by a specific author.)
I already knew this... perhaps because I had already dealt with other forums.
Now, I don't see any advantage in clicking this icon and only seeing my posts. If you skip to my last post you are fine. Now just my posts? I think it doesn't make sense. But maybe I'm the one who doesn't understand the point.