The down arrow is tiny, requiring you to be quite precise. This coupled with the requirement of two clicks, makes it mildly annoying if you repeat it often. Aside from that, what one would expect is a commonly-used feature is hidden inside a menu.
There is, but it's quite small and doesn't show you a complete list of the new posts. It's useful for people who spend a lot of time on the forum but not those of us who visit once per day or so.
Thanks for this, that's slightly better. However, it's not in a prominent position and it looks like a header, not a link. Also, the page it links to is not the same as the New Posts page. It shows you all activity in chronological order, whereas New Posts shows you only those threads with activity since you last hit Mark as Read.