Hello and welcome to TerraForums shoutbox 2.0 lol. First off, make sure you check out all the neat customization available to you by clicking on the notice at the top of the shoutbox (currently says "Click here to change personal settings").
Let me know if you have any questions, but I will answer one... No, there isn't an option to have the posts/new topics show up on the side like the old one. It WILL pop up a notification within the shouts so you will see it when you're in the shoutbox... You'll get many other notifications here too, like when you get a forum PM! If you like to have a spot to go and see forum activity without searching around like the olden days... go up to "New Posts" in the top left corner of the forum and click "What's new?" OR "New Posts" check both of them out and see which you like better.