Re: Forum icons for new posts
For sidebars you need to look into using either widget logic plugins, or simply creating your own child theme and inserting a bbPress sidebar instead of the default one. Not to hard to do, but way more involved than I care to try and answer in a post.
There are a number of classes in the code for the posts such as sticky, super-sticky, etc, but there are currently no classes or functions for determining if the user has read a topic or not.
Believe it or not, that type of functionality is very intensive. Imagine a board with 50k members and millions of posts. Trying to keep track of exactly what posts each user has seen and has not seen really fills the db up very fast.
Now this is possible of course with plugin territory so it is possible as most forums do this. I can say though, I personally at least am glad it is not in the core as I do NOT want that kind of overhead for my rather large forums. Also considering I have friends whose forums are 10x my size, I can only imagine the nightmare.